the measure theoretic identity underlying transient fluctuation theorems we prove a measure theoretic identity that underlies all transient fluctuation theorems tfts for entropy production and dissipated work in inhomogeneous deterministic and stochastic processes including those of evans and searles crooks and seifert the identity is used to deduce a tautological physical interpretation of tfts in terms of the arrow of time and its generality reveals that the self inverse nature of the various trajectory and process transformations historically relied upon to prove tfts while necessary for these theorems from a physical standpoint it is however not necessary from a mathematical one the moment generating functions of thermodynamic variables appearing in the identity are shown to converge in general only in a vertical strip in the complex plane with the consequence that a tft that holds over arbitrary timescales may fail to give rise to an asymptotic fluctuation theorem for any possible speed of the corresponding large deviation principle the case of strongly biased birth death chains is presented to illustrate this phenomenon we also discuss insights obtained from our measure theoretic formalism into the results of saha et al on the breakdown of tfts for driven brownian particles

lmi based robust control of fractional order uncertain linear systems this paper concerns with the method of observer based control and static output feedback control for fractional order uncertain systems with the fractional commensurate order a 0 a 1 and a email protected email protected 2 via linear matrix inequality lmi approach respectively first the sufficient conditions for robust asymptotical stability of the closed loop control systems are presented next by using matrix s singular value decomposition svd and lmi technics the existence condition and method of designing a robust stabilizing controller for such fractional order control systems are derived unlike previous methods the results are obtained in terms of lmi which can be easily obtained by matlab s lmi toolbox finally two numerical examples demonstrate the validity of this approach

asymptotics of work distributions in nonequilibrium systems the asymptotic behavior of the work distribution in driven nonequilibrium systems is determined using the method of optimal fluctuations for systems described by langevin dynamics the corresponding euler lagrange equation together with the appropriate boundary conditions and an equation for the leading pre exponential factor are derived the method is applied to three representative examples and the results are used to improve the accuracy of free energy estimates based on the application of the jarzynski equation

fluctuation theorems and atypical trajectories in this work we have studied simple models that can be solved analytically to illustrate various fluctuation theorems these fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work wc thermodynamic work w total entropy stot and dissipated heat q when the system is driven arbitrarily out of equilibrium all these quantities can be defined for individual trajectories we have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level as the time of observation increases the fraction of such atypical trajectories decreases as expected at the macroscale the distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak most probable value in the atypical regime without violating the expected average behaviour however dissipated heat and classical work exhibit a peak in the regime of typical behaviour only

an optimization problem with applications to optimal design theory on utilise les resultats d un probleme d optimisation pour montrer que pour certains plans s ils sont optimaux relativement a deux criteres alors ils sont optimaux relativement a plusieurs autres criteres

brief paper pseudo state feedback stabilization of commensurate fractional order systems this paper addresses the problem of pseudo state feedback stabilization of commensurate fractional order systems fos in the proposed approach linear matrix inequalities lmi formalism is used to check if the pseudo state matrix eigenvalues belong to the fos stability region of the complex plane a review of lmi stability conditions is first proposed for fractional order 0 n 1 and 1 n 2 the paper then focuses particularly on the case 0 n 1 as the stability region is non convex and associated lmi condition is not as straightforward to obtain as in the case 1 n 2 a new lmi stability condition is thus proposed based on this condition a necessary and sufficient lmi method for the design of stabilizing controllers is given this method paves the way for extension to fos of various lmi based results among these possible extensions a first result on robust control of polytopic fractional order systems is given in this paper

robust stability and stabilization of fractional order interval systems with the fractional order alpha the 0 alpha 1 case this technical note firstly presents a sufficient and necessary condition for the robust asymptotical stability of fractional order interval systems with the fractional order satisfying 0 1 and then a sufficient condition for the robust asymptotical stabilization of such fractional order interval systems is derived all the results are obtained in terms of linear matrix inequalities finally two illustrative examples are given to show that our results are effective for checking the robust stability and designing the robust stabilizing controller for fractional order interval systems

asymptotical stabilization of fractional order linear systems in triangular form in this paper both state and output feedback stabilization controllers are designed for triangular fractional order linear time invariant fo lti systems with fractional order 0 a 2 by introducing appropriate transformations of coordinates the problems of control design are converted into the problems of finding some parameters which can be certainly obtained by solving relevant matrix inequalities contrary to many existing linear matrix inequalities lmis based approaches all the matrix inequalities involved for the systems under study always have feasible solutions a simulation example is given to demonstrate the effectiveness of the proposed controllers

work fluctuations in a time dependent harmonic potential rigorous results beyond the overdamped limit we investigate the stochastic motion of a brownian particle in the harmonic potential with a time dependent force constant it may describe the motion of a colloidal particle in an optical trap where the potential well is formed by a time dependent field we use the path integral formalism to solve the langevin equation and the associated fokker planck kramers equation rigorous relations are derived to generate the probability density function for the time dependent nonequilibrium work production beyond the overdamped limit we find that the work distribution exhibits an exponential tail with a power law prefactor accompanied by an interesting oscillatory feature multiple pseudo locking unlocking transitions due to the inertial effect some exactly solvable cases are discussed in the overdamped limit

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

exact results for the finite time thermodynamic uncertainty relation we obtain exact results for the recently discovered finite time thermodynamic uncertainty relation for the dissipated work w d in a stochastically driven system with non gaussian work statistics

power fluctuation theorem for a brownian oscillator in a thermal bath in this paper we prove the validity of the total power fluctuation theorem for a brownian particle in a harmonic trap when it is dragged out of equilibrium taking into account the inertia term in the langevin equation we first consider the theorem for an ordinary brownian harmonic oscillator embedded in a thermal bath as a second case we assume the presence of an electromagnetic field acting on the charged brownian oscillator in both cases the theorem is proved for two examples in the trap motion linear and oscillatory drag on the potential minimum

anomalous fluctuation properties we complement and extend our work on fluctuations arising in nonequilibrium systems in steady states driven by l evy noise h touchette and e g d cohen phys rev e 76 020101 r 2007 as a concrete example we consider a particle subjected to a drag force and a l evy white noise with tail index ensuremath mu 0 2 and calculate the probability distribution of the work done on the particle by the drag force as well as the probability distribution of the work dissipated by the dragged particle in a nonequilibrium steady state for 0l ensuremath mu l2 both distributions satisfy what we call an anomalous fluctuation property characterized by positive and negative fluctuations that asymptotically have the same probability for ensuremath mu 2 by contrast the work and dissipated work distributions satisfy the known conventional and extended fluctuation relations respectively which are both characterized by positive fluctuations that are exponentially more probable than negative fluctuations the difference between these different fluctuation behaviors is discussed in the context of large deviation theory experiments that could probe or reveal an anomalous fluctuation property are also discussed

lmi stability conditions for fractional order systems after an overview of the results dedicated to stability analysis of systems described by differential equations involving fractional derivatives also denoted fractional order systems this paper deals with linear matrix inequality lmi stability conditions for fractional order systems under commensurate order hypothesis it is shown that a direct extension of the second lyapunov s method is a tedious task if the fractional order n is such that 0 n 1 the stability domain is not a convex region of the complex plane however through a direct stability domain characterization three lmi stability analysis conditions are proposed the first one is based on the stability domain deformation and the second one on a characterization of the instability domain which is convex the third one is based on generalized lmi framework these conditions are applied to the gain margin computation of a crone suspension

technical communique necessary and sufficient stability condition of fractional order interval linear systems this paper establishes a necessary and sufficient stability condition of fractional order interval linear systems it is supposed that the system matrix a is an interval uncertain matrix and fractional commensurate order belongs to email protected email protected 2 using the existence condition of hermitian p p for a complex lyapunov inequality we prove that the fractional order interval linear system is robust stable if and only if there exists hermitian matrix p p such that a certain type of complex lyapunov inequality is satisfied for all vertex matrices the results are directly extended to the robust stability condition of fractional order interval polynomial systems

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 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

zon cohen singularity and negative inverse temperature in a trapped particle limit we study a brownian particle on a moving periodic potential we focus on the statistical properties of the work done by the potential and the heat dissipated by the particle when the period and the depth of the potential are both large by using a boundary layer analysis we calculate a cumulant generating function and a biased distribution function the result allows us to understand a zon cohen singularity for an extended fluctuation theorem from a viewpoint of rare trajectories characterized by a negative inverse temperature of the biased distribution function

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

finite time stabilization of fractional order uncertain chain of integrator an integral sliding mode approach in this technical note a novel methodology for robust finite time stabilization of a chain of uncertain fractional order integrator is proposed this is achieved by first designing a nominal controller which stabilizes the system in finite time an integral sliding mode like surface and a switching controller is proposed such that when the system is on the surface the equivalent value of the integral sliding mode control is the negative of the disturbance and hence the disturbance is cancelled an improved strategy with more general kind of uncertainty is also proposed numerical examples are presented to illustrate the proposed methods

large deviations in the alternating mass harmonic chain we extend the work of kannan et al and derive the cumulant generating function cgf for the alternating mass harmonic chain consisting of n particles and driven by heat reservoirs the main result is a closed expression for the cgf in the thermodynamic large n limit this expression is independent of n but depends on whether the chain consists of an even or odd number of particles in accordance with the results obtained by kannan et al for the heat current this result is in accordance with the absence of local thermodynamic equilibrium in a linear system

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