stochastic flow cascades we introduce and explore a stochastic flow cascade sfc model a general statistical model for the unidirectional flow through a tandem array of heterogeneous filters examples include the flow of i liquid through heterogeneous porous layers ii shocks through tandem shot noise systems iii signals through tandem communication filters the sfc model combines together the langevin equation convolution filters and moving averages and poissonian randomizations a comprehensive analysis of the sfc model is carried out yielding closed form results levy laws are shown to universally emerge from the sfc model and characterize both heavy tailed retention times noah effect and long ranged correlations joseph effect

stretching based diagnostics and reduction of chemical kinetic models with diffusion a new method for diagnostics and reduction of dynamical systems and chemical kinetic models is proposed the method makes use of the local structure of the normal stretching rates by projecting the dynamics onto the local directions of maximal stretching the approach is computationally very simple as it implies the spectral analysis of a symmetric matrix notwithstanding its simplicity stretching based analysis derives from a geometric basis grounded on the pointwise applications of concepts of normal hyperbolicity theory as a byproduct a simple reduction method is derived equivalent to a local embedding algorithm which is based on the local projection of the dynamics onto the most unstable and or slow modes compared to the time scale dictated by the local tangential dynamics this method provides excellent results in the analysis and reduction of dynamical systems displaying relaxation towards an equilibrium point limit cycles and chaotic attractors several numerical examples deriving from typical models of reaction diffusion kinetics exhibiting complex dynamics are thoroughly addressed the application to typical combustion models is also analyzed

robust designs based on the infinitesimal approach abstract we introduce an infinitesimal approach to the construction of robust designs for linear models the resulting designs are robust against small departures from the assumed linear regression response and or small departures from the assumption of uncorrelated errors subject to satisfying a robustness constraint they minimize the determinant of the mean squared error matrix of the least squares estimator at the ideal model the robustness constraint is quantified in terms of boundedness of the gateaux derivative of this determinant in the direction of a contaminating response function or autocorrelation structure specific examples are considered if the aforementioned bounds are sufficiently large then permutations of the classically optimal designs which minimize variance alone at the ideal model meet our robustness criteria otherwise new designs are obtained

optimal experimental designs in the flow rate of particles this article focuses on analyzing the process of jam formation during the discharge by gravity of granular material stored in a two dimensional silo the aim of the article is two fold first optimal experimental designs are computed in which four approaches are considered d optimality a combination of d optimality and a cost gain function bayesian d optimality and sequential designing these results reveal that the efficiency of the design used by the experimenters can be improved dramatically a sensitivity analysis with respect to the most important parameter is also performed second estimation of the unknown parameters is done using least squares that is assuming normality and also via maximum likelihood assuming the exponential distribution simulations for the designs considered in this article show that the variance the mean squared error and the bias of the estimators using maximum likelihood are in most cases lower than those using least squares supplementary materials for this arti

experimental study of the fluctuation theorem in a nonequilibrium steady state the fluctuation theorem ft quantifies the probability of second law violations in small systems over short time scales while this theorem has been experimentally demonstrated for systems that are perturbed from an initial equilibrium state there are a number of studies suggesting that the theorem applies asymptotically in the long time limit to systems in a nonequilibrium steady state the asymptotic application of the ft to such nonequilibrium steady states has been referred to in the literature as the steady state fluctuation theorem or ssft in this paper we demonstrate experimentally the application of the ft to nonequilibrium steady states using a colloidal particle localized in a translating optical trap furthermore we show for this colloidal system that the ft holds under nonequilibrium steady states for all time and not just in the long time limit as in the ssft

direct evaluation of large deviation functions we introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities such as current or density that are local in time the large deviation functions are given in terms of the typical properties of a modified dynamics and since they no longer involve rare events can be evaluated efficiently and over a wider ranges of values we illustrate the method with the current fluctuations of the totally asymmetric exclusion process and with the work distribution of a driven lorentz gas

finite size scaling of current fluctuations in the totally asymmetric exclusion process we study the fluctuations of the current j t of the totally asymmetric exclusion process with open boundaries using a density matrix renormalization group approach we calculate the cumulant generating function of the current this function can be interpreted as a free energy for an ensemble in which histories are weighted by exp sj t we show that in this ensemble the model has a first order spacetime phase transition at s 0 we numerically determine the finite size scaling of the cumulant generating function near this phase transition both in the non equilibrium steady state and for large times

sociophysics of sexism normal and anomalous petrie multipliers a recent mathematical model by karen petrie explains how sexism towards women can arise in organizations where male and female are equally sexist indeed the petrie model predicts that such sexism will emerge whenever there is a male majority and quantifies this majority bias by the petrie multiplier the square of the male female ratio in this paper emulating the shift from normal to anomalous diffusion we generalize the petrie model to a stochastic poisson model that accommodates heterogeneously sexist men and woman and that extends the normal quadratic petrie multiplier to anomalous non quadratic multipliers the petrie multipliers span a full spectrum of behaviors which we classify into four universal types a variation of the stochastic poisson model and its petrie multipliers is further applied to the context of cyber warfare

steady states invariant measures and response theory using the method of computer simulation we test the predictions of nonlinear response theory for classical systems subject to dissipative external fields we provide convincing numerical evidence that kawasaki methods agree with both the transient time correlation function predictions and with a direct measurement of the nonlinear response furthermore this numerical agreement is observed over a time scale which is sufficiently long for the response to have relaxed to within ensuremath sim 1 of its nonequilibrium steady state value this is in spite of the fact that in the steady state the n particle distribution function ultimately becomes fractal we discuss the normalization of the kawasaki distribution and derive a lagrangian form of the kawasaki response function and show that it is consistent with predictions that are obtained using a natural invariant measure for nonequilibrium steady states c 1995 the american physical society

causality response theory and the second law of thermodynamics we show that there is a close connection between the assumption of causality and the second law of thermodynamics we also show that for a class of classical reversible deterministic systems it is overwhelmingly improbable either to find causal steady states that violate the second law or anticausal states that satisfy the second law these arguments indicate that the existence of and the sign associated with the second law of thermodynamics is ultimately determined by causality our discussion employs a green kubo relation that we derive for an anticausal linear transport coefficient

on the definition of entropy production via examples we present a definition of entropy production rate for classes of deterministic and stochastic dynamics the point of departure is a gibbsian representation of the steady state path space measure for which the density is determined with respect to the time reversed process the gibbs formalism is used as a unifying algorithm capable of incorporating basic properties of entropy production in nonequilibrium systems our definition is motivated by recent work on the gallavotti cohen local fluctuation theorem and it is illustrated via a number of examples

the tasaki crooks quantum fluctuation theorem starting out from the recently established quantum correlation function expression of the characteristic function for the work performed by a force protocol on the system in talkner et al 2007 phys rev e 75 050102 preprint cond mat 0703213 the quantum version of the crooks fluctuation theorem is shown to emerge almost immediately by the mere application of an inverse fourier transformation

on detailed balance and reversibility of semi markov processes and single molecule enzyme kinetics semi markov processes have found increasing applications in modeling the kinetics of single enzyme molecules detailed balance is a widely accepted condition for markov models of closed chemical systems and well known to be equivalent to the reversibility of a stationary markov process we show that for a semi markov process detailed balance is only a necessary condition but not sufficient for its time reversibility the statistical independence between the transition direction and the sojourn time is also necessary we show that the direction time independence naturally arises from the exit problem of markov models for enzyme kinetics with detailed balance detailed balance and the direction time independence together are equivalent to the time reversibility of a stationary semi markov process applications of the present theory to single molecule enzymology are also presented

necessary and sufficient conditions for the two point phase probability function of two phase random media constructing realizations of random media with a specified two point phase probability function s2 has attracted considerable attention in the recent literature however little is known about cond

higher order corrections in the approximation of low dimensional manifolds and the construction of simplified problems with the csp method in systems of stiff ordinary differential equations odes both fast and slow time scales are encountered the fast time scales are responsible for the development of low dimensional manifolds on which the solution moves according to the slow time scales in this paper methodologies for constructing highly accurate i expressions describing the manifold and ii simplified non stiff equations governing the slow evolution of the solution on the manifold are developed according to an iterative procedure proposed in the computational singular perturbation csp method it is shown that the increasing accuracy achieved with each iteration is directly related to the time rates of change of the csp vectors spanning the manifold along the solution trajectory here an algorithm is presented which implements these calculations and is validated on the basis of two simple examples

nonlinear experiments optimal design and inference based on likelihood abstract nonlinear experiments involve response and regressors that are connected through a nonlinear regression type structure examples of nonlinear models include standard nonlinear regression logistic regression probit regression poisson regression gamma regression inverse gaussian regression and so on the fisher information associated with a nonlinear experiment is typically a complex nonlinear function of the unknown parameter of interest as a result we face an awkward situation designing an efficient experiment will require knowledge of the parameter but the purpose of the experiment is to generate data to yield parameter estimates our principal objective here is to investigate proper designing of nonlinear experiments that will let us construct efficient estimates of parameters we focus our attention on a very general nonlinear setup that includes many models commonly encountered in practice the experiments considered have two fundamental stages a static design in the initial stage

illustrative example of the relationship between dissipation and relative entropy kawai parrondo and van den broeck phys rev lett 98 080602 2007 have recently established a quantitative relationship between dissipated work and a microscopic information theoretic measure of irreversibility we illustrate this result using the exactly solvable system of a brownian particle in a dragged harmonic trap

stochastic solution of space time fractional diffusion equations classical and anomalous diffusion equations employ integer derivatives fractional derivatives and other pseudodifferential operators in space in this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are mittag leffler type this leads to explicit solutions for space time fractional diffusion equations with multiscaling space fractional derivatives and additional insight into the meaning of these equations

on the covariance function of stationary binary sequences with given mean recent work on characterizing the covariance functions of stationary binary sequences has been geometric in flavor extreme distributions induced in windows of a given length are obtained from special periodic sequences the work is extended to sequences with a given mean m revealing some finer structure

on the validity of entropy production principles for linear electrical circuits we explain the non validity of close to equilibrium entropy production principles in the context of linear electrical circuits both the minimum and the maximum entropy production principles are understood within dynamical fluctuation theory the starting point are langevin equations obtained by combining kirchoff s laws with a johnson nyquist noise at each dissipative element in the circuit the main observation is that the fluctuation functional for time averages that can be read off from the path space action is in first order around equilibrium given by an entropy production rate

the quasi steady state assumption a case study in perturbation the quasi steady state assumption qssa of biochemistry is studied as an approximation that is important in itself and also that exemplifies an approach to ode systems with an initial fast transient simple estimates of the two relevant time scales of the underlying problem are made these estimates lead to a dimensionless formulation containing a different small parameter from that which is customary earlier results on the qssa are surveyed in the context of the new nondimensionalization it is shown that more comprehensive and simpler error estimates can now be made some general methodological hints are drawn from this example

smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics this paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics we adopt a new point of view which has emerged progressively in recent years and which takes seriously into account the chaotic character of the microscopic time evolution the emphasis is on nonequilibrium steady states rather than the traditional approach to equilibrium point of view of boltzmann the nonequilibrium steady states in presence of a gaussian thermostat are described by srb measures in terms of these one can prove the gallavotti cohen fluctuation theorem one can also prove a general linear response formula and study its consequences which are not restricted to near equilibrium situations at equilibrium one recovers in particular the onsager reciprocity relations under suitable conditions the nonequilibrium steady states satisfy the pairing theorem of dettmann and morriss the results just mentioned hold so far only for classical systems they do not involve large size i e they hold without a thermodynamic limit

the explicit form of the rate function for semi markov processes and its contractions we derive the explicit form of the rate function for semi markov processes here the random time change trick plays an essential role also by exploiting the contraction principle of the large deviation theory to the explicit form we show that the fluctuation theorem gallavotti cohen symmetry holds for semi markov cases furthermore we elucidate that our rate function is an extension of the level 2 5 rate function for markov processes to semi markov cases

current fluctuations in stochastic systems with long range memory we propose a method to calculate the large deviations of current fluctuations in a class of stochastic particle systems with history dependent rates long range temporal correlations are seen to alter the speed of the large deviation function in analogy with long range spatial correlations in equilibrium systems we give some illuminating examples and discuss the applicability of the gallavotti cohen fluctuation theorem

unraveling the large deviation statistics of markovian open quantum systems we analyze dynamical large deviations of quantum trajectories in markovian open quantum systems in their full generality we derive a quantum level 2 5 large deviation principle for these systems which describes the joint fluctuations of time averaged quantum jump rates and of the time averaged quantum state for long times like its level 2 5 counterpart for classical continuous time markov chains which it contains as a special case this description is both explicit and complete as the statistics of arbitrary time extensive dynamical observables can be obtained by contraction from the explicit level 2 5 rate functional we derive our approach uses an unraveled representation of the quantum dynamics which allows these statistics to be obtained by analyzing a classical stochastic process in the space of pure states for quantum reset processes we show that the unraveled dynamics is semi markovian and derive bounds on the asymptotic variance of the number of quantum jumps which generalize classical thermodynamic uncertainty relations we finish by discussing how our level 2 5 approach can be used to study large deviations of nonlinear functions of the state such as measures of entanglement

some optimal designs for repeated measurements with autoregressive errors summary a number of individuals are observed at equally spaced time points different individuals behave independently but the observations on the same individual have the autocorrelation structure of a first order autoregressive process we are concerned with the optimal allocation of treatments assuming that at each time point a new selection must be made conditions for optimality are given for models without nuisance parameters and also with covariates and with block effects

temporal disorder and fluctuation theorem in chemical reactions we report the analytical study of a class of chemical reactions described as birth and death stochastic processes ruled by a master equation compatible with the mass action law of chemical kinetics we solve analytically this master equation to find the generating functions of the fluctuating fluxes and of the lebowitz spohn action functional these generating functions are explicitly shown to obey fluctuation theorems in the case of fluxes we derive relations for the nonlinear response coefficients extending onsager s reciprocity relations moreover symmetry relations reminiscent of the fluctuation theorem are obtained for the finite time probability distributions of the fluxes the temporal disorder of the stochastic process is also characterized and related to the thermodynamic entropy production

wamr an adaptive wavelet method for the simulation of compressible reacting flow part i accuracy and efficiency of algorithm abstract the wavelet adaptive multiresolution representation wamr method provides a robust method for controlling spatial grid adaptation fine grid spacing in regions where a solution varies greatly i e near steep gradients or near singularities and a much coarser grid where the solution varies slowly subsequently a wide range of spatial scales often demanded in challenging continuum physics problems can be efficiently captured furthermore the wavelet transform provides a direct measure of local error at each collocation point effectively producing automatically verified solutions the method is applied to the solution of unsteady compressible reactive flow equations and includes detailed diffusive transport and chemical kinetics models accuracy and performance of the method are examined on several test problems the sparse grids produced by the wamr method exhibit an impressive compression of the solution reducing the number of collocation points used by factors of many orders of magnitude when compared to uniform grids of equivalent resolution

explicit time scale splitting algorithm for stiff problems auto ignition of gaseous mixtures behind a steady shock a new explicit algorithm based on the computational singular perturbation csp method is presented this algorithm is specifically designed to solve stiff problems and its performance increases with stiffness the key concept in its structure is the splitting of the fast from the slow time scales in the problem realized by embedding csp concepts into an explicit scheme in simple terms the algorithm marches in time with only the terms producing the slow time scales while the contribution of the terms producing the fast time scales is taken into account at the end of each integration step as a correction the new algorithm is designed for the integration of stiff systems of pdes by means of explicit schemes for simplicity in the presentation and discussion of the different features of the new algorithm a simple test case is considered involving the auto ignition of a methane air mixture behind a normal shock wave which is described by a system of odes the performance of the new algorithm accuracy and computational efficiency is then compared with the well known lsode package its merits when used for the solution of systems of pdes are discussed although when dealing with a stiff system of odes the new algorithm is shown to provide equal accuracy with that delivered by lsode at the cost of higher execution time the results indicate that its performance could be superior when facing a stiff system of pdes

contrasts under long range correlations the background of the paper is the empirical observation from a variety of subject areas that long range correlations appear to be much more frequent than has been previously assumed this includes high quality measurement series which are commonly treated as prototypes of i i d observations evidence is briefly cited in the paper it has already been shown elsewhere that long range dependence leads to results that can be qualitatively different from those obtained under short range dependence and in particular that long range dependence has drastic effects on the naive statistical treatment of absolute constants the natural question arising from this also of relevance for statistical practice is how the long range dependence affects the statistics for contrasts the main answer given in this paper is twofold

approximation of slow and fast dynamics in multiscale dynamical systems by the linearized relaxation redistribution method in this paper we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation ode system towards a stable low dimensional invariant manifold in the phase space slow invariant manifold sim as a result the demanding problem of constructing sim of any dimensions is recast into the remarkably simpler task of solving a properly devised ode system by stiff numerical schemes available in the literature in the same spirit a set of equations is elaborated for local construction of the fast subspace and possible initialization procedures for the above equations are discussed the implementation to a detailed mechanism for combustion of hydrogen and air has been carried out while a model with the exact chapman enskog solution of the invariance equation is utilized as a benchmark

characterizing the autocorrelations of binary sequences the class of autocorrelation functions of binary sequences is studied in terms of their finite dimensional projections that is the vector ranges of finite sets of consecutive correlation coefficients these are convex polyhedra whose extreme points can be generated by binary sequences of bounded periods algorithms are given for the calculation of the extreme points tables are presented for the extreme points and supporting hyperplanes of projections of dimensions up to five some conclusions about the general class of autocorrelations of binary sequences are drawn from these tables

on the entropy production of time series with unidirectional linearity there are non gaussian time series that admit a causal linear autoregressive moving average arma model when regressing the future on the past but not when regressing the past on the future the reason is that in the latter case the regression residuals are not statistically independent of the regressor in previous work we have experimentally verified that many empirical time series indeed show such a time inversion asymmetry

universal cumulants of the current in diffusive systems on a ring we calculate exactly the first cumulants of the integrated current and of the activity which is the total number of changes of configurations of the symmetric simple exclusion process on a ring with periodic boundary conditions our results indicate that for large system sizes the large deviation functions of the current and of the activity take a universal scaling form with the same scaling function for both quantities this scaling function can be understood either by an analysis of bethe ansatz equations or in terms of a theory based on fluctuating hydrodynamics or on the macroscopic fluctuation theory of bertini de sole gabrielli jona lasinio and landim

continuous time random walk for open systems fluctuation theorems and counting statistics we consider continuous time random walks ctrw for open systems that exchange energy and matter with multiple reservoirs each waiting time distribution wtd for times between steps is characterized by a positive parameter alpha which is set to alpha 1 if it decays at least as fast as t 2 at long times and therefore has a finite first moment a wtd with alpha 1 decays as t alpha 1 a fluctuation theorem for the trajectory quantity r defined as the logarithm of the ratio of the probability of a trajectory and the probability of the time reversed trajectory holds for any ctrw however r can be identified as a trajectory entropy change only if the wtds have alpha 1 and satisfy separability also called direction time independence for nonseparable wtds with alpha 1 r can only be identified as a trajectory entropy change at long times and a fluctuation theorem for the entropy change then only holds at long times for wtds with 0 alpha 1 no meaningful fluctuation theorem can be derived we also show that the experimentally accessible nth moments of the energy and matter transfers between the system and a given reservoir grow as t nalpha at long times

optimum biased coin designs for sequential clinical trials with prognostic factors patients in a clinical trial arrive sequentially and are assigned to one of t treatments this assignment should maintain a balance between the numbers receiving each treatment yet should be sufficiently random to avoid any suspicion of conscious or unconscious cheating to balance these requirements efron 1971 introduced biased coin designs for the comparison of two treatments in which allocation of the treatment is determined probabilistically but with a bias towards the underrepresented treatment one disadvantage of efron s scheme is that it does not include balance over covariates or prognostic factors which may affect the response of the patient to the treatment biased coin schemes which do force balance over both treatments and prognostic factors are given by pocock simon 1975 and efron 1980 the properties of the designs have been elucidated by numerical studies and they are now being increasingly used in clinical trials reviews of the literature and discussions of the practical implications of the designs are given by pocock 1979 and simon 1979 however the designs suffer from the disadvantage that they rely on arbitrary functions to achieve the desired balance the procedures thus lack a firm theoretical framework an alternative approach in the presence of prognostic factors begg iglewicz 1980 uses optimum design theory to suggest a deterministic design criterion which is then modified for computational convenience in this paper i use optimum design theory to provide a procedure of the biased coin type for an arbitrary number of treatments in the presence or absence of prognostic factors this has the theoretical advantage of obviating dependence on a series of arbitrary functions the necessary optimum design theory is presented in 2 and in 3 applied to biased coin experiments the simplest case that of two treatments in the absence of prognostic factors is studied in 4 the extension to three or more treatments is in 5 followed in 6 by the allowance for prognostic factors although in the biased coin designs allocation of treatments is made probabilistically the results of the paper can be used for the sequential construction of da optimum designs in which randomization is not introduced by the experimenter all the designs mentioned so far are sequential but not adaptive in the useful distinction made by pericchi 1981 they are data dependent but not outcomedependent each allocation depends on the previous allocations and prognostic factors

non markovianity and negative entropy production rates entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems its positivity can be ensured for a wide class of setups but the entropy production rate can become negative sometimes this is often taken as an indicator of non markovianity we make this link precise by showing under which conditions a negative entropy production rate implies non markovianity and when it does not for a system coupled to a single heat bath this can be established within a unified language for two setups i the dynamics resulting from a coarse grained description of a markovian master equation and ii the classical hamiltonian dynamics of a system coupled to a bath the quantum version of the latter result is shown not to hold despite the fact that the integrated thermodynamic description is formally equivalent to the classical case the instantaneous fixed point of a non markovian dynamics plays an important role in our study our key contribution is to provide a consistent theoretical framework to study the finite time thermodynamics of a large class of dynamics with a precise link to its non markovianity

on the optimality of finite williams ii a designs on considere des plans de type ii a de williams et on s interesse a l autoregression du premier ordre stationnaire avec 0

random walk to a nonergodic equilibrium concept random walk models such as the trap model continuous time random walks and comb models exhibit weak ergodicity breaking when the average waiting time is infinite the open question is what statistical mechanical theory replaces the canonical boltzmann gibbs theory for such systems in this paper a nonergodic equilibrium concept is investigated for a continuous time random walk model in a potential field in particular we show that in the nonergodic phase the distribution of the occupation time of the particle in a finite region of space approaches u or w shaped distributions related to the arcsine law we show that when conditions of detailed balance are applied these distributions depend on the partition function of the problem thus establishing a relation between the nonergodic dynamics and canonical statistical mechanics in the ergodic phase the distribution function of the occupation times approaches a ensuremath delta function centered on the value predicted based on standard boltzmann gibbs statistics the relation of our work to single molecule experiments is briefly discussed

minimum entropy production principle from a dynamical fluctuation law the minimum entropy production principle provides an approximative variational characterization of close to equilibrium stationary states both for macroscopic systems and for stochastic models analyzing the fluctuations of the empirical distribution of occupation times for a class of markov processes we identify the entropy production as the large deviation rate function up to leading order when expanding around a detailed balance dynamics in that way the minimum entropy production principle is recognized as a consequence of the structure of dynamical fluctuations and its approximate character gets an explanation we also discuss the subtlety emerging when applying the principle to systems whose degrees of freedom change sign under kinematical time reversal

entropy production in the majority vote model we analyzed the entropy production in the majority vote model by using a mean field approximation and monte carlo simulations the dynamical rules of the model do not obey detailed balance so that entropy is continuously being produced this nonequilibrium stochastic model is known to have a critical behavior belonging to the universality class of the equilibrium ising model we show that the entropy production exhibits a singularity at the critical point whose exponent is estimated numerically

computation of current cumulants for small nonequilibrium systems we analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems recently discussed in the framework of full counting statistics for mesoscopic systems this method is based on identifying the current cumulants from a rayleigh schrodinger perturbation expansion for the generating function here it is derived from a simple path distribution identity and extended to the joint statistics of multiple currents for a possible thermodynamical interpretation we compare this approach to a generalized onsager machlup formalism we present calculations for a boundary driven kawasaki dynamics on a one dimensional chain both for attractive and repulsive particle interactions

generalized master equation via aging continuous time random walks this article discusses the problem of the equivalence between continuous time random walk ctrw and generalized master equation gme

the g scheme a framework for multi scale adaptive model reduction the numerical solution of mathematical models for reaction systems in general and reacting flows in particular is a challenging task because of the simultaneous contribution of a wide range of time scales to the system dynamics however the dynamics can develop very slow and very fast time scales separated by a range of active time scales an opportunity to reduce the complexity of the problem arises when the fast active and slow active time scales gaps becomes large we propose a numerical technique consisting of an algorithmic framework named the g scheme to achieve multi scale adaptive model reduction along with the integration of the differential equations des the method is directly applicable to initial value odes and by using the method of lines pdes we assume that the dynamics is decomposed into active slow fast and when applicable invariant subspaces the g scheme introduces locally a curvilinear frame of reference defined by a set of orthonormal basis vectors with corresponding coordinates attached to this decomposition the evolution of the curvilinear coordinates associated with the active subspace is described by non stiff des whereas that associated with the slow and fast subspaces is accounted for by applying algebraic corrections derived from asymptotics of the original problem adjusting the active des dynamically during the time integration is the most significant feature of the g scheme since the numerical integration is accomplished by solving a number of des typically much smaller than the dimension of the original problem with corresponding saving in computational work to demonstrate the effectiveness of the g scheme we present results from illustrative as well as from relevant problems

dynamical fluctuations for semi markov processes wedevelopanonsager machlup typetheoryfornonequilibriumsemi markov processes our main result is an exact large time asymptotics for the joint probability of the occupation times and the currents in the system establishing some generic large deviation structures we discuss in detail how the nonequilibrium driving and the non exponential waiting time distribution influence the occupation current statistics the violation of the markov condition is reflected in the emergence of a new type of nonlocality in the fluctuations explicit solutions are obtained for some examples of driven random walks on the ring

computational singular perturbation analysis of stochastic chemical systems with stiffness abstract computational singular perturbation csp is a useful method for analysis reduction and time integration of stiff ordinary differential equation systems it has found dominant utility in particular in chemical reaction systems with a large range of time scales at continuum and deterministic level on the other hand csp is not directly applicable to chemical reaction systems at micro or meso scale where stochasticity plays an non negligible role and thus has to be taken into account in this work we develop a novel stochastic computational singular perturbation scsp analysis and time integration framework and associated algorithm that can be used to not only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems but also analyze the dynamics of the reduced stochastic reaction systems the algorithm is illustrated by an application to a benchmark stochastic differential equation model and numerical experiments are carried out to demonstrate the effectiveness of the construction

fluctuation of the entropy production for the lorentz gas under small external forces in this paper we study the physical and statistical properties of the periodic lorentz gas with finite horizon driven to a non equilibrium steady state by the combination of non conservative external forces and deterministic thermostats a version of this model was introduced by chernov eyink lebowitz and sinai and subsequently generalized by chernov and the third author non equilibrium steady states for these models are srb measures and they are characterized by the positivity of the steady state entropy production rate our main result is to establish that the entropy production in this context equal to the phase space contraction satisfies the gallavotti cohen fluctuation relation the main tool needed in the proof is the family of anisotropic banach spaces introduced by the first and third authors to study the ergodic and statistical properties of billiards using transfer operator techniques

time reversal and entropy there is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time reversal symmetry and the entropy production in such processes we explain on an elementary mathematical level the relations between entropy production phase space contraction and time reversal starting from a deterministic dynamics both closed and open systems in the transient and in the steady regime are considered the main result identifies under general conditions the statistical mechanical entropy production as the source term of time reversal breaking in the path space measure for the evolution of reduced variables this provides a general algorithm for computing the entropy production and to understand in a unified way a number of useful in equalities we also discuss the markov approximation important are a number of old theoretical ideas for connecting the microscopic dynamics with thermodynamic behavior

exact equalities and thermodynamic relations for nonequilibrium steady states we study thermodynamic operations which bring a nonequilibrium steady state ness to another ness in physical systems under nonequilibrium conditions we model the system by a suitable markov jump process and treat thermodynamic operations as protocols according to which the external agent varies parameters of the markov process then we prove among other relations a ness version of the jarzynski equality and the extended clausius relation the latter can be a starting point of thermodynamics for ness we also find that the corresponding nonequilibrium entropy has a microscopic representation in terms of symmetrized shannon entropy in systems where the microscopic description of states involves momenta all the results in the present paper are mathematically rigorous

large deviations in weakly interacting boundary driven lattice gases one dimensional boundary driven lattice gases with local interactions are studied in the weakly interacting limit the density profiles and the correlation functions are calculated to first order in the interaction strength for zero range and short range processes differing only in the specifics of the detailed balance dynamics furthermore the effective free energy large deviation function and the integrated current distribution are also found to this order from the former we find that the boundary drive generates long range correlations only for the short range dynamics while the latter provides support to an additivity principle recently proposed by bodineau and derrida

an information theory approach to nonlinear nonequilibrium thermodynamics using the problem of ion channel thermodynamics as an example we illustrate the idea of building up complex thermodynamic models by successively adding physical information we present a new formulation of information algebra that generalizes methods of both information theory and statistical mechanics from this foundation we derive a theory for ion channel kinetics identifying a nonequilibrium process free energy functional in addition to the well known integrated work functionals the gibbs maxwell relation for the free energy functional is a green kubo relation applicable arbitrarily far from equilibrium that captures the effect of non local and time dependent behavior from transient thermal and mechanical driving forces comparing the physical significance of the lagrange multipliers to the canonical ensemble suggests definitions of nonequilibrium ensembles at constant capacitance or inductance in addition to constant resistance our result is that statistical mechanical descriptions derived from a few primitive algebraic operations on information can be used to create experimentally relevant and computable models by construction these models may use information from more detailed atomistic simulations two surprising consequences to be explored in further work are that in distinguishability factors are automatically predicted from the problem formulation and that a direct analogue of the second law for thermodynamic entropy production is found by considering information loss in stochastic processes the information loss identifies a novel contribution from the instantaneous information entropy that ensures non negative loss

large deviation function for entropy production in driven one dimensional systems the large deviation function for entropy production is calculated by solving a time independent eigenvalue problem for a particle driven along a periodic potential in an intermediate force regime the large deviation function shows pronounced deviations from a gaussian behavior with a characteristic kink at zero entropy production such a feature can also be extracted from the analytical solution of the asymmetric random walk to which the driven particle can be mapped in a certain parameter range

ribosome dwell times and the protein copy number distribution translation is the cellular process in which ribosomes make proteins from information encoded on messenger rna mrna we model translation with an exclusion process taking into account the experimentally determined non exponential waiting time between steps of a ribosome from numerical simulations using realistic parameter values we determine the distribution p e of the number of proteins e produced by one mrna we find that for small e this distribution is not geometric we present a simplified and analytically solvable model that relates p e to the distributions of the times to produce the first e proteins

fluctuation theorems for entropy production and heat dissipation in periodically driven markov chains asymptotic fluctuation theorems are statements of a gallavotti cohen symmetry in the rate function of either the time averaged entropy production or heat dissipation of a process such theorems have been proved for various general classes of continuous time deterministic and stochastic processes but always under the assumption that the forces driving the system are time independent and often relying on the existence of a limiting ergodic distribution in this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous time processes without a stationary distribution considering specifically a finite state markov chain driven by periodic transition rates we find that for both entropy production and heat dissipation the usual gallavotti cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process in which the trajectory and the driving protocol have been time reversed the effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process and vice versa revealing that the distributions of fluctuations in universes in which time moves forward and backward are related as an additional result the asymptotic time averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics

on the reversibility of the observed process of three state hidden markov model for the continuous time and the discrete time three state hidden markov model the flux of the likelihood function up to 3 dimensional of the observed process is shown explicitly as an application the sufficient and necessary condition of the reversibility of the observed process is shown

natural tangent dynamics with recurrent biorthonormalizations a geometric computational approach to dynamical systems exhibiting slow manifolds and periodic chaotic limit sets abstract this article develops a geometric method referred to as natural tangent dynamics with recurrent biorthonormalizations ntdrb that unifies into a single computational technique the analysis of dynamical systems possessing either a slow manifold associated with an equilibrium point or exhibiting nontrivial limit sets limit cycles and chaotic attractors for the first class of systems the main focus relies on the identification of the slow fast timescales while for the latter dynamics within nontrivial attractors the central issue is the temporal dichotomy between unstable stable components as described by the structure of the lyapunov spectrum the method is based on vector and covector dynamics in the tangent and cotangent bundles induced by the phase space flow and on the periodic application of a biorthonormalization procedure which contrasts the natural tendencies of vectors and covectors to align towards the most unstable slow subspaces the ntdrb method provides the most convenient and natural vector and covector bases for i the characterization of the fast timescales controlling the dynamic relaxation towards a slow manifold ii the identification of the stable and unstable components of the dynamics on a limit set iii the construction of a low dimensional reduced model reproducing the asymptotic behavior of the original systems

a d optimal design for estimation of parameters of an exponential linear growth curve of nanostructures we consider the problem of determining an optimal experimental design for estimation of parameters of a class of complex curves characterizing nanowire growth that is partially exponential and partially linear locally d optimal designs for some of the models belonging to this class are obtained by using a geometric approach further a bayesian sequential algorithm is proposed for obtaining d optimal designs for models with a closed form solution and for obtaining efficient designs in situations where theoretical results cannot be obtained the advantages of the proposed algorithm over traditional approaches adopted in recently reported nanoexperiments are demonstrated using monte carlo simulations the computer code implementing the sequential algorithm is available as supplementary materials

microscopic origins of irreversible macroscopic behavior time asymmetric behavior as embodied in the second law of thermodynamics is observed in individual macroscopic systems it can be understood as arising naturally from time symmetric microscopic laws in accord with the ideas of thompson maxwell and boltzmann alternative explanations based on equating irreversible macroscopic behavior with the mixing type of behavior already present in the time evolution of ensembles probability distributions of certain systems having only a few degrees of freedom are in my opinion unnecessary misguided and misleading

mathematical formalism for isothermal linear irreversibility we prove the equivalence among symmetricity time reversibility and zero entropy production of the stationary solutions of linear stochastic differential equations a sufficient and necessary rever

fitness response relation of a multitype age structured population dynamics we construct a pathwise formulation for a multitype age structured population dynamics which involves an age dependent cell replication and transition of gene or phenotypes by employing the formulation we derive a variational representation of the stationary population growth rate the representation comprises a tradeoff relation between growth effects and a single cell intrinsic dynamics described by a semi markov process this variational representation leads to a response relation of the stationary population growth rate in which statistics on a retrospective history work as the response coefficients these results contribute to predicting and controlling growing populations based on experimentally observed cell lineage information

optimal designs for radiation retention with poisson correlated response in this paper we describe a non linear model with correlated observations which accounts for the elimination rate of radiation in the lung of individuals who have been exposed to an accidental intake at some time the response is then modelled as a conditional poisson distribution when the leak is moderate or the size of the particles is large a theoretical justification of this assumption is given and d optimal designs are computed

frenetic bounds on the entropy production we give a systematic derivation of positive lower bounds for the expected entropy production ep rate in classical statistical mechanical systems obeying a dynamical large deviation principle the logic is the same for the return to thermodynamic equilibrium as it is for steady nonequilibria working under the condition of local detailed balance we recover there recently studied uncertainty relations for the ep appearing in studies about the effectiveness of mesoscopic machines in general our refinement of the positivity of the expected ep rate is obtained in terms of a positive and even function of the expected current s which measures the dynamical activity in the system a time symmetric estimate of the changes in the system s configuration also underdamped diffusions can be included in the analysis

a hierarchical kinetic theory of birth death and fission in age structured interacting populations we develop mathematical models describing the evolution of stochastic age structured populations after reviewing existing approaches we formulate a complete kinetic framework for age structured interacting populations undergoing birth death and fission processes in spatially dependent environments we define the full probability density for the population size age chart and find results under specific conditions connections with more classical models are also explicitly derived in particular we show that factorial moments for non interacting processes are described by a natural generalization of the mckendrick von foerster equation which describes mean field deterministic behavior our approach utilizes mixed type multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy bbgky like equation hierarchies

subordination to periodic processes and synchronization abstract we study the subordination to a process that is periodic in the natural time scale and equivalent to a clock with n states the rationale for this investigation is given by a set of many interacting clocks with n states the natural time scale representation corresponds to the dynamics of an individual clock with no interaction with the other clocks of this set we argue that the cooperation among the clocks of this set has the effect of generating a global clock whose times of sojourn in each of its n states are described by a distribution density with an inverse power law form and power index 2 this is equivalent to extending the widely used subordination method from fluctuation dissipation processes to periodic processes thereby raising the question of whether special conditions exist of perfect synchronization signaled by regular oscillations and especially by oscillations with no damping we study first the case of a poisson subordination function we show that in spite of the random nature of the subordination method the procedure has the effect of creating damped oscillations whose damping vanishes in the limiting case of n 1 thereby suggesting a condition of perfect synchronization in this limit the bateman s mathematical arguments h bateman higher transcendental functions vol iii robert k krieger publishing company inc krim fr drive malabar fl copyright 1953 by mcgraw hill book company inc indicate that the condition of perfect synchronization is possible also in the non poisson case with 2 although it may lie beyond the range of computer simulation to make the theoretical predictions accessible to numerical simulation we use a subordination function whose survival probability is a mittag leffler exponential function this method prevents us from directly establishing the macroscopic coherence emerging from 2 which generates a perfect form of 1 f noise however it affords indirect evidence that perfect synchronization signaled by undamped regular oscillations may be produced in this case furthermore we explore a condition characterized by an excellent agreement between theory and numerical simulation where the long time region relaxation with a perfect inverse power law decay emerging from the subordination to ordinary fluctuation dissipation processes is replaced by exponentially damped regular oscillations

current large deviations for asymmetric exclusion processes with open boundaries we study the large deviation functional of the current for the weakly asymmetric simple exclusion process in contact with two reservoirs we compare this functional in the large drift limit to the one of the totally asymmetric simple exclusion process in particular to the jensen varadhan functional conjectures for generalizing the jensen varadhan functional to open systems are also stated

the transient fluctuation theorem of sample entropy production for general stochastic processes the transient fluctuation theorem for stochastic processes was first put forward by d j searles and d j evans 1999 in the present paper it is rigorously proved that the transient fluctuation theorem tft of sample entropy production which is previously defined by jiang et al 2003 and reid et al 2005 and also called the general action functional up to boundary terms by lebowitz and spohn 1999 holds for general stochastic processes without the assumption of markovian homogeneous or stationary properties then the condition of our theorem is verified for various stochastic processes including homogeneous inhomogeneous markov chains and general diffusion processes among these cases the transient fluctuation theorems for inhomogeneous markov chains and general diffusion processes are rigorously derived for the first time

fluctuation theorems for non markovian quantum processes exploiting previous results on markovian dynamics and fluctuation theorems we study the consequences of memory effects on single realizations of nonequilibrium processes within an open system approach the entropy production along single trajectories for forward and backward processes is obtained with the help of a recently proposed classical like non markovian stochastic unravelling which is demonstrated to lead to a correction of the standard entropic fluctuation theorem this correction is interpreted as resulting from the interplay between the information extracted from the system through measurements and the flow of information from the environment to the open system due to memory effects single realizations of a dynamical process are no longer independent and their correlations fundamentally affect the behavior of entropy fluctuations

current fluctuations in the one dimensional symmetric exclusion process with open boundaries we calculate the first four cumulants of the integrated current of the one dimensional symmetric simple exclusion process of n sites with open boundary conditions for large system size n the generating function of the integrated current depends on the densities a and b of the two reservoirs and on the fugacity z the parameter conjugated to the integrated current through a single parameter based on our expressions for these first four cumulants we make a conjecture which leads to a prediction for all the higher cumulants in the case a 1 and b 0 our conjecture gives the same universal distribution as the one obtained by lee levitov and yakovets for one dimensional quantum conductors in the metallic regime

black scholes model under subordination abstract in this paper we consider a new mathematical extension of the black scholes bs model in which the stochastic time and stock share price evolution is described by two independent random processes the parent process is brownian and the directing process is inverse to the totally skewed strictly stable process the subordinated process represents the brownian motion indexed by an independent continuous and increasing process this allows us to introduce the long term memory effects in the classical bs model

generalization of the dynamical lack of fit reduction from generic to generic the lack of fit statistical reduction developed and formulated first by bruce turkington is a general method taking liouville equation for probability density detailed level and transforming it to reduced dynamics of projected quantities less detailed level in this paper the method is generalized the hamiltonian liouville equation is replaced by an arbitrary hamiltonian evolution combined with gradient dynamics generic the boltzmann entropy is replaced by an arbitrary entropy and the kinetic energy by an arbitrary energy the gradient part is a generalized gradient dynamics generated by a dissipation potential the reduced evolution of the projected state variables is shown to preserve the generic structure of the original detailed level evolution the dissipation potential is obtained by solving a hamilton jacobi equation in summary the lack of fit reduction can start with generic and obtain generic for the reduced state variables

fluctuation theorem for currents and schnakenberg network theory a fluctuation theorem is proved for the macroscopic currents of a system in a nonequilibrium steady state by using schnakenberg network theory the theorem can be applied in particular in reaction systems where the affinities or thermodynamic forces are defined globally in terms of the cycles of the graph associated with the stochastic process describing the time evolution

non equilibrium current fluctuations in stochastic lattice gases we study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles more precisely we establish a large deviation principle for a space time fluctuation j of the empirical current with a rate functional i j we then estimate the probability of a fluctuation of the average current over a large time interval this probability can be obtained by solving a variational problem for the functional i we discuss several possible scenarios interpreted as dynamical phase transitions for this variational problem they actually occur in specific models we finally discuss the time reversal properties of i and derive a fluctuation relationship akin to the gallavotti cohen theorem for the entropy production