rare event sampling for driven inertial systems via the nonequilibrium distribution function recently substantial generalizations have been made to the yamada kawasaki type nonlinear response theory formalism for deterministic dynamics these provide opportunities to develop new importance sampling techniques against known distribution functions we exploit this to develop a method of calculating nonequilibrium rate constants across a large free energy barrier allowing molecular simulations to access far greater time scales in contrast to existing stochastic methods we do not merely follow the dynamics forward in time allowing systems governed by inertial equations of motion to be usefully addressed we further generalize the yamada kawasaki type formalism to the case of stochastic equations of motion and the resulting nonequilibrium importance sampling method follows straight forwardly we quantitatively test the method on stochastic and deterministic models specifically chosen to allow a comparison with reliable independently obtained data to do this we consider oscillators in a one dimensional double well potential either side of the well is separated by an energy barrier and the oscillator is driven away from equilibrium by a position dependent temperature profile the energy barrier is chosen to be low enough that we can still solve the system computationally by brute force we demonstrate that the results of our method are consistent with those from the brute force simulations to very high accuracy we also show how our method is more than two orders of magnitude more efficient for the given example than forward flux sampling

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

method of and device for speech signal coding and decoding by subband analysis and vector quantization with dynamic bit allocation according to the coding method the digital speech signal is split into subbands each subband is coded independently of the others the first two subbands undergo an adaptive linear prediction operation yielding a residual normalized with respect to a quantized r m s value the residual samples are quantized and coded by a variable bit number as to the third subband the samples normalized with respect to a quantized gain term are directly quantized and coded by a variable bit number while splitting the subband signals into sample blocks for the first two subbands the coefficient vectors of subband linear prediction filters relevant to each block are also determined by vector quantization and linear prediction inverse filtering operations quantized r m s values are also determined to calculate the numbers of bits permitting subband signals coding the coded signal consists of subband signal quantization level indices of r m s value quantization level indices and of linear prediction filter coefficient vector indices

reflexive derivations and lattices of invariant subspaces of operator algebras associated with them the paper studies unbounded reflexive derivations of c algebras of bounded operators on hilbert spaces h whose domains d are weekly dense in b h and contain compact operators it describes a one to one correspondence between these derivations and pairs s l where s are symmetric densely operators on h and l are j orthogonal reflexive lattices of subspaces in the deficiency spaces of s the domains d of these derivations are associated with some non selfadjoint reflexive algebras a of bounded operators on h h the paper analyzes the structure of the lattices of invariant subspaces of a and of the normalizers of a the largest lie subalgebras of b h h such that a are their lie ideals

note on the kaplan yorke dimension and linear transport coefficients a number of new relations between the kaplan yorke dimension phase space contraction transport coefficients and the maximal lyapunov exponents are given for dissipative thermostatted systems subject to a small but non zero external field in a nonequilibrium stationary state a condition for the extensivity of phase space dimension reduction is given a new expression for the linear transport coefficients in terms of the kaplan yorke dimension is derived alternatively the kaplan yorke dimension for a dissipative macroscopic system can be expressed in terms of the linear transport coefficients of the system the agreement with computer simulations for an atomic fluid at small shear rates is very good

chaotic principle an experimental test abstract the chaotic hypothesis discussed in gallavotti and cohen 1995 is tested experimentally in a simple conduction model besides a confirmation of the hypothesis predictions the results suggest the validity of the hypothesis in the much wider context in which as the forcing strength grows the attractor ceases to be an anosov system and becomes an axiom a attractor a first text of new predictions is also attempted

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

dimension formula for random transformations we consider compositions of random diffeomorphisms and show that the dimension of sample measures equals lyapunov dimension as conjectured in the nonrandom case by yorke et al

symmetric operator extensions of unbounded derivations of c algebras abstract let be a closed derivation from a c subalgebra a of b h into b h and let there exist a closed symmetric operator s such that is that is for a d ad s d s and a d s i s a d s symmetric extensions of s are investigated i e such symmetric extensions t of s that it in particular it is shown that if s has equal and finite deficiency indices and if i a and a does not have finite dimensional representations a c h for example then there exists a self adjoint extension of s

acoustic signal transform coding method and decoding method having a high efficiency envelope flattening method therein an input acoustic signal is subjected to modified discrete cosine transform processing to obtain its spectrum characteristics linear prediction coefficients are derived from the input acoustic signal in a linear prediction coding analysis part and the prediction coefficients are subjected to fourier transform in a spectrum envelope calculation part to obtain the envelope of the spectrum characteristics of the input acoustic signal in a normalization part the spectrum characteristics are normalized by the envelope thereof to obtain residual coefficients another normalization part normalizes the residual coefficients by a residual coefficients envelope predicted in a residual coefficients envelope calculation part thereby obtaining fine structure coefficients which are vector quantized in a quantization part a de normalization part de normalizes the quantized fine structure coefficients the residual coefficients envelope calculation part uses the reproduced residual coefficients to predict the envelope of residual coefficients of the subsequent frame

coexistence of chaotic and non chaotic states in the two dimensional gauss navier stokes dynamics recently gallavotti proposed an equivalence conjecture in hydrodynamics which states that forced damped fluids can be equally well represented by means of the navier stokes equations ns and by means of time reversible modifications of ns called gauss navier stokes equations gns this equivalence conjecture received numerical support in several recent papers concerning two dimensional fluid mechanics the corresponding results rely on the fact that the ns and gns systems only have one attracting set performing similar two dimensional simulations we find that there are conditions to be met by the gns system for this to be the case in particular increasing the reynolds number while keeping fixed the number of fourier modes leads to the coexistence of different attractors this makes difficult a test of the equivalence conjecture but constitutes a spurious effect due to the insufficient spectral resolution with sufficiently fine spectral resolution the steady states are unique and the equivalence conjecture can be conveniently established

comments on the entropy of nonequilibrium steady states we discuss the entropy of nonequilibrium steady states we analyze the so called spontaneous production of entropy in certain reversible deterministic nonequilibrium system and its link with the collapse of such systems towards an attractor that is of lower dimension than the dimension of phase space this means that in the steady state limit the gibbs entropy diverges to negative infinity we argue that if the gibbs entropy is expanded in a series involving 1 2 body terms the divergence of the gibbs entropy is manifest only in terms involving integrals whose dimension is higher than approximately the kaplan yorke dimension of the steady state attractor all the low order terms are finite and sum in the weak field limit to the local equilibrium entropy of linear irreversible thermodynamics

ergodicity ensembles irreversibility in boltzmann and beyond the contents of a not too well known paper by boltzmann are critically examined the etymology of the word ergodic and its implications are discussed a connection with the modern theory of ruelle is attempted

a dynamical systems interpretation of the dissipation function t mixing and their relation to thermodynamic relaxation we review the notions of the dissipation function and t mixing for non invariant measures recently introduced for nonequilibrium molecular dynamics models we provide a dynamical systems interpretation for the dissipation function and related results providing new perspectives into results such as the second law inequality we then consider the problem of relaxation within this framework the convergence of time averages along single phase space trajectories as opposed to the convergence of ensemble averages as a first step in this direction we observe that t mixing implies convergence to a unique asymptotic ensemble independent on the initial ensemble in particular the initial ensemble can be concentrated arbitrarily closely to any point in phase space

on the fluctuation relation for nose hoover boundary thermostated systems we discuss the transient and steady state fluctuation relation for a mechanical system in contact with two deterministic thermostats at different temperatures the system is a modified lorentz gas in which the fixed scatterers exchange energy with the gas of particles and the thermostats are modelled by two nose hoover thermostats applied at the boundaries of the system the transient fluctuation relation which holds only for a precise choice of the initial ensemble is verified at all times as expected times longer than the mesoscopic scale needed for local equilibrium to be settled are required if a different initial ensemble is considered this shows how the transient fluctuation relation asymptotically leads to the steady state relation when as explicitly checked in our systems the condition found in d j searles et al j stat phys 128 1337 2007 for the validity of the steady state fluctuation relation is verified for the steady state fluctuations of the phase space contraction rate and of the dissipation function a similar relaxation regime at shorter averaging times is found the quantity satisfies with good accuracy the fluctuation relation for times larger than the mesoscopic time scale the quantity appears to begin a monotonic convergence after such times this is consistent with the fact that and differ by a total time derivative and that the tails of the probability distribution function of are gaussian

note on two theorems in nonequilibrium statistical mechanics an attempt is made to clarify the difference between a theorem derived by evans and searles in 1994 on the statistics of trajectories in phase space and a theorem proved by the authors in 1995 on the statistics of fluctuations on phase space trajectory segments in a nonequilibrium stationary state

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

superderivations of c algebras implemented by symmetric operators the paper studies unbounded symmetric and dissipative implementations s g of superderivations ofc algebras mathfrak u it associates with them representations s of the domainsd of on the deficiency spacesn s of the symmetric operatorss a link is obtained between the deficiency indicesn s ofs and the dimensions of irreducible representations of mathfrak u for the case when s g is a maximal implementation and max n s some conditions are given for the representation s to be semisimple and to extend to a bounded representation of mathfrak u

the metric entropy of diffeomorphisms part ii relations between entropy exponents and dimension on considere f m m m m un c 2 diffeomorphisme f d une variete de riemann compacte m preservant une mesure de probabilite de borel m soit hm f l entropie metrique de f et 1 x r x x les exposants de lyapunov distincts en x on etablit une formule qui relie h m f et les r x x

on the asymptotic convergence of the transient and steady state fluctuation theorems nonequilibrium molecular dynamics simulations are used to demonstrate the asymptotic convergence of the transient and steady state forms of the fluctuation theorem in the case of planar poiseuille flow we find that the transient form valid for all times converges to the steady state predictions on microscopic time scales further we find that the time of convergence for the two theorems coincides with the time required for satisfaction of the asymptotic steady state fluctuation theorem

equilibrium fluctuation relations and transport for irreversible deterministic dynamics abstract in a recent paper m colangeli et al j stat mech p04021 2011 it was argued that the fluctuation relation for the phase space contraction rate could suitably be extended to non reversible dissipative systems we strengthen here those arguments providing analytical and numerical evidence based on the properties of a simple irreversible nonequilibrium baker model we also consider the problem of response showing that the transport coefficients are not affected by the irreversibility of the microscopic dynamics in addition we prove that a form of detailed balance hence of equilibrium holds in the space of relevant variables despite the irreversibility of the phase space dynamics this corroborates the idea that the same stochastic description which arises from a projection onto a subspace of relevant coordinates is compatible with quite different underlying deterministic dynamics in other words the details of the microscopic dynamics are largely irrelevant for what concerns properties such as those concerning the fluctuation relations the equilibrium behavior and the response to perturbations

dynamical system models of transport chaos characteristics the macroscopic limit and irreversibility the escape rate formalism and the thermostating algorithm describe relaxation towards a decaying state with absorbing boundaries and a steady state of periodic systems respectively it has been shown that the key features of the transport properties of both approaches if modeled by low dimensional dynamical systems can conveniently be described in the framework of multibaker maps in the present paper we discuss in detail the steps required to reach a meaningful macroscopic limit the limit involves a sequence of coarser and coarser descriptions projections until one reaches the level of irreversible macroscopic advection diffusion equations the influence of boundary conditions is studied in detail only a few of the chaos characteristics possess a meaningful macroscopic limit but none of these is sufficient to determine the entropy production in a general non equilibrium state 2003 elsevier b v all rights reserved

fluctuation relation beyond linear response theory the fluctuation relation fr is an asymptotic result onthe distribution of certain observables averaged over timeintervals as and it is a generalization of thefluctuation dissipation theorem to far from equilibrium systemsin a steady state which reduces to the usual green kubo gk relation in the limit of small external non conservative forces fr is a theorem for smooth uniformly hyperbolic systems and it isassumed to be true in all dissipative chaotic enough systemsin a steady state in this paper we develop a theory of finitetime corrections to fr needed to compare the asymptoticprediction of fr with numerical observations which necessarilyinvolve fluctuations of observables averaged over finite timeintervals we perform a numerical test of fr in two cases inwhich non gaussian fluctuations are observable while gk does notapply and we get a non trivial verification of fr that is independent of and different from linear response theory our results are compatible with the theory of finite timecorrections to fr while fr would be observably violated well within the precision of our experiments if such correctionswere neglected

totally symmetric algebras and the similarity problem abstract for closed derivations on b h the algebras a a o a a a d are considered a new involution is introduced in b h h such that a a and that a is totally symmetric if is a closed involution it is proved that if an invertible operator belongs to d sca then its inverse also belongs to d sca for f a i f a where f are selfadjoint operators it is shown that a f are reflexive semi simple and totally symmetric algebras if f is unbounded then a f has a strictly irreducible representation which is not similar to representations

a local fluctuation theorem abstract a mechanism for the validity of a local version of the fluctuation theorem uniform in the system size is discussed for a reversible chain of weakly coupled anosov systems

on typicality in nonequilibrium steady states from the statistical mechanical viewpoint relaxation of macroscopic systems and response theory rest on a notion of typicality according to which the behavior of single macroscopic objects is given by appropriate ensembles ensemble averages of observable quantities represent the measurements performed on single objects because almost all objects share the same fate in the case of non dissipative dynamics and relaxation toward equilibrium states almost all is referred to invariant probability distributions that are absolutely continuous with respect to the lebesgue measure in other words the collection of initial micro states single systems that do not follow the ensemble is supposed to constitute a set of vanishing phase space volume this approach is problematic in the case of dissipative dynamics and relaxation to nonequilibrium steady states because the relevant invariant distributions attribute probability 1 to sets of zero volume while evolution commonly begins in equilibrium states i e in sets of full phase space volume we consider the relaxation of classical thermostatted particle systems to nonequilibrium steady states we show that the dynamical condition known as omega t mixing is necessary and sufficient for relaxation of ensemble averages to steady state values moreover we find that the condition known as weak t mixing applied to smooth observables is sufficient for ensemble relaxation to be independent of the initial ensemble lastly we show that weak t mixing provides a notion of typicality for dissipative dynamics that is based on the non invariant lebesgue measure and that we call physical ergodicity

speech analysis synthesis method and apparatus therefor an impulse sequence of a pitch frequency is detected from a phase equalized prediction residual of an input speech signal s t and a quasi periodic impulse sequence is obtained by processing the impulse sequence so that a fluctuation in its pitch frequency is within an allowed limit range the magnitudes of the quasi periodic impulse sequence are so determined as to minimize an error between the waveform of a synthesized speech obtainable by exciting an all pole filter 18 with the quasi periodic impulse sequence and the waveform of a phase equalized speech obtainable by applying the input speech signal to a phase equalizing filter 5 preferably the quasi periodic impulse sequence is supplied to the all pole filter after being applied to a zero filter 10 in which it is given features of the prediction residual of the speech coefficients of the zero filter are also determined so that the error of the waveforms of the synthesized speech and the phase equalized speech is minimum

dynamic bit allocation subband excited transform coding method and apparatus in an adaptive subband excited transform speech encoding system a range of quantizers are available and are dynamically selected for each window of speech the quantizers designated for individual subbands are determined to minimize mean squared error distortion in the recreated signal while using no more than a predetermined number of quantization bits per window of speech

synchronisation of canonical measures for hyperbolic attractors under suitable conditions it is shown how to change the velocity of ac2 axioma attractor so that the sinai ruelle bowen measure coincides with the measure of maximal entropy these measures are obtained as limits of certain closed orbital measures

extended heat fluctuation theorems for a system with deterministic and stochastic forces heat fluctuations over a time tau in a nonequilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components a brownian particle dragged through a fluid by a harmonic potential which is moved with constant velocity using a langevin equation we find the exact fourier transform of the distribution of these fluctuations for all tau by a saddle point method we obtain analytical results for the inverse fourier transform which for not too small tau agree very well with numerical results from a sampling method as well as from the fast fourier transform algorithm due to the interaction of the deterministic part of the motion of the particle in the mechanical potential with the stochastic part of the motion caused by the fluid the conventional heat fluctuation theorem is for infinite and for finite tau replaced by an extended fluctuation theorem that differs noticeably and measurably from it in particular for large fluctuations the ratio of the probability for absorption of heat by the particle from the fluid to the probability to supply heat by the particle to the fluid is much larger here than in the conventional fluctuation theorem

the role of the number of degrees of freedom and chaos in macroscopic irreversibility abstract this article aims at revisiting with the aid of simple and neat numerical examples some of the basic features of macroscopic irreversibility and thus of the mechanical foundation of the second principle of thermodynamics as drawn by boltzmann emphasis will be put on the fact that in systems characterized by a very large number of degrees of freedom irreversibility is already manifested at a single trajectory level for the vast majority of the far from equilibrium initial conditions a property often referred to as typicality we also discuss the importance of the interaction among the microscopic constituents of the system and the irrelevance of chaos to irreversibility showing that the same irreversible behaviors can be observed both in chaotic and non chaotic systems

extension of derivations in the algebra of compact operators let c h denote the c algebra of all compact linear operators on a complex hilbert space h if is a closable derivation in c h which anti commutes with an involutive antiautomorphism and has finite spatial deficiency indices then there exists an infinitesimal generator 0 of a continuous action of r on c h which extends and anti commutes with this is an analogue of the von neumann s theorem which states that a symmetric operator commuting with a conjugation j has a self adjoint extension which also commutes with j

the steady state fluctuation relation for the dissipation function we give a proof of transient fluctuation relations for the entropy production dissipation function in nonequilibrium systems which is valid for most time reversible dynamics we then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax producing a unique nonequilibrium steady state although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown if such a steady state exists the generation of the steady state fluctuation relation from the transient relation is shown to be very general it is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation which is needed also for e g the existence of transport coefficients because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities the steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor whose convergence is problematic for systems close to equilibrium we examine some model dynamics that have been considered previously and show how they are described in the context of this work

fluctuation theorem for stochastic systems the fluctuation theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics it has been proved in a number of different ways for thermostatted deterministic nonequilibrium systems in the present paper we show that the fluctuation theorem is also valid for a class of stochastic nonequilibrium systems the theorem is therefore not reliant on the reversibility or the determinism of the underlying dynamics numerical tests verify the theoretical result

application of the gallavotti cohen fluctuation relation to thermostated steady states near equilibrium the fluctuation relation of the gallavotti cohen fluctuation theorem gcft concerns fluctuations in the phase space compression rate of dissipative reversible dynamical systems it has been proven for anosov systems but it is expected to apply more generally this raises the question of which non anosov systems satisfy the fluctuation relation we analyze time dependent fluctuations in the phase space compression rate of a class of n particle systems that are at equilibrium or in near equilibrium steady states this class does not include anosov systems or isoenergetic systems however it includes most steady state systems considered in molecular dynamics simulations of realistic systems we argue that the fluctuations of the phase space compression rate of these systems at or near equilibrium do not satisfy the fluctuation relation of the gcft although the discrepancies become somewhat smaller as the systems move further from equilibrium in contrast similar fluctuation relations for an appropriately defined dissipation function appear to hold both near and far from equilibrium

fluctuation theorems for entropy production in open systems we derive a fluctuation theorem to describe entropy fluctuations in steady states of systems with density gradients due to open boundaries the fluctuations are related to the growth rate of the phase space density instead of the phase space contraction rate explicit derivations are presented for a multibaker map but the arguments are rather general and should hold for a much wider class of dynamical systems a comparison with recent results for stochastic systems is also given

lyapunov spectra and nonequilibrium ensembles equivalence in 2d fluid mechanics we perform numerical experiments to study the lyapunov spectra of dynamical systems associated with the navier stokes ns equation in two spatial dimensions truncated over the fourier basis recently new equations called gns equations have been introduced and conjectured to be equivalent to the ns equations at large reynolds numbers the lyapunov spectra of the ns and of the corresponding gns systems overlap adding evidence in favor of the conjectured equivalence already studied and partially extended in previous papers we make use of the lyapunov spectra to study a fluctuation relation which had been proposed to extend the fluctuation theorem to strongly dissipative systems preliminary results towards the formulation of a local version of the fluctuation formula are also presented

methods and apparatus for reconstructing non quantized adaptively transformed voice signals reconstructing adaptively transformed voice signals is done using noise shaping 110 to scale the spectral envelope 98 before generating the bit allocation 111 generating discrete cosine transform coefficents 80 is accomplished by determining from the bit allocation 111 to which of the transform coefficients 80 no bits were allocated retrieving the spectral envelope information 98 corresponding to the transform coefficients 80 to which no bits are allocated and substituting each item of spectral envelope information 98 into the block of quantized 82 transform coefficients 80 after each item has been given a sign and scaled

chaotic hypothesis fluctuation theorem and singularities the chaotic hypothesis has several implications which have generated interest in the literature because of their generality and because a few exact predictions are among them however its application to physics problems requires attention and can lead to apparent inconsistencies in particular there are several cases that have been considered in the literature in which singularities are built in the models for instance when among the forces there are lennard jones potentials which are infinite in the origin and the constraints imposed on the system do not forbid arbitrarily close approach to the singularity even though the average kinetic energy is bounded the situation is well understood in certain special cases in which the system is subject to gaussian noise here the treatment of rather general singular systems is considered and the predictions of the chaotic hypothesis for such situations are derived the main conclusion is that the chaotic hypothesis is perfectly adequate to describe the singular physical systems we consider ie deterministic systems with thermostat forces acting according to gauss principle for the constraint of constant total kinetic energy isokinetic gaussian thermostats close and far from equilibrium near equilibrium it even predicts a fluctuation relation which in deterministic cases with more general thermostat forces ie not necessarily of gaussian isokinetic nature extends recent relations obtained in situations in which the thermostatting forces satisfy gauss principle this relation agrees where expected with the fluctuation theorem for perfectly chaotic systems the results are compared with some recent works in the literature

reversibility coarse graining and the chaoticity principle we describe a way of interpreting the chaotic principle of gc1 more extensively than it was meant in the original works mathematically the analysis is based on the dynamical notions of axiom a and axiom b and on the notion of axiom c that we introduce arguing that it is suggested by the results of an experiment bgg on chaotic motions physically we interpret a breakdown of the anosov property of a time reversible attractor replaced as a control parameter changes by an axiom a property as a spontaneous breakdown of the time reversal symmetry the relation between time reversal and the symmetry that remains after the breakdown is analogous to the breakdown of t invariance while tcp still holds

time dependent response theory and nonequilibrium free energy relations the mathematics of time dependent nonlinear response theory frequently leads to results which although formally exact are not amenable to experimental application or even to use in computer simulations here we give a rigorous derivation of a tractable expression for the thermostatted nonlinear response of classical many body systems to time dependent dissipative fields the theory also allows for the concurrent parametric transformation of the system hamiltonian our analysis shows once again the intimate relationship between nonequilibrium free energy relations such as the jarzynski equality and nonlinear response theory we make a few remarks concerning the maximum entropy production approximation

on the concept of attractor this note proposes a definition for the concept of attractor based on the probable asymptotic behavior of orbits the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor

dynamical ensembles equivalence in fluid mechanics abstract an attempt to put together various theoretical mathematical or experimental results recently developed in apparently unrelated subjects namely ruelle s 1980 approach to turbulence the body of nose hoover type of molecular dynamics experiments evans and morriss 1990 evans et al 1993 bonetto et al 1996 mathematical results on lyapunov exponents the pairing rule dressler 1988 and dettman and morriss 1995 and experimental results on them sarman et al 1992 bohr et al 1996 theoretical as well as mathematical results on fluctuations frisch and parisi 1984 multifractality and gallavoti and cohen 1995 chaotic hypothesis the key idea that we try to clarify is that of dynamical ensembles as a generalization of the classical equilibrium ensembles arguing that they should be identified with the srb distributions and that they share several properties with the classical ensembles most of the results invoked here did not deal directly with the navier stokes equations and yet they seem to have a lot to do with them as we shall argue here the discussion will focus on the navier stokes and dissipative euler equations with the aim of proposing several experiments apt to test the equivalence of dynamical ensembles and the chaotic hypothesis the ideas developed to a great extent from the efforts put in interpreting the experimental results in bonetto et al 1996