Related papers: Big Entropy Fluctuations in Statistical Equilibriu…
The structure of very complicated irregular "microscopic" (local) entropy fluctuations around a big separated "macroscopic" (global) fluctuation in the statistical equilibrium was studied in numerical experiments on a simple 2--freedom…
Large entropy fluctuations in a nonequilibrium steady state of classical mechanics were studied in extensive numerical experiments on a simple 2-freedom model with the so-called Gauss time-reversible thermostat. The local fluctuations (on a…
Within the abstract framework of dynamical system theory we describe a general approach to the Transient (or Evans-Searles) and Steady State (or Gallavotti-Cohen) Fluctuation Theorems of non-equilibrium statistical mechanics. Our main…
Nonequilibrium complex systems are often effectively described by the mixture of different dynamics on different time scales. Superstatistics, which is "statistics of statistics" with two largely separated time scales, offers a consistent…
We investigate the statistics of recurrences to finite size intervals for chaotic dynamical systems. We find that the typical distribution presents an exponential decay for almost all recurrence times except for a few short times affected…
The celebrated Evans-Searles, respectively Gallavotti-Cohen, fluctuation theorem concerns certain universal statistical features of the entropy production rate of a classical system in a transient, respectively steady, state. In this paper,…
We study analytically giant fluctuations and temporal intermittency in a stochastic one-dimensional model with diffusion and aggregation of masses in the bulk, along with influx of single particles and outflux of aggregates at the…
Fluctuations of observables as functions of time, or "fluctuation patterns", are studied in a chaotic microscopically reversible system that has irreversibly reached a nonequilibrium stationary state. Supposing that during a certain, long…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…
We study non-equilibrium statistical mechanics of a Gaussian dynamical system and compute in closed form the large deviation functionals describing the fluctuations of the entropy production observable with respect to the reference state…
A dynamical system that undergoes a supercritical Hopf's bifurcation is perturbed by a multiplicative Brownian motion that scales with a small parameter $\epsilon$. The random fluctuations of the system at the critical point are studied…
We formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within…
The fluctuation relations have received considerable attention since their emergence and development in the 1990s. We present a summary of the main results and suggest ways to interpret this material. Starting with a consideration of the…
Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…
While entropy changes are the usual subject of fluctuation theorems, we seek fluctuation relations involving time-symmetric quantities, namely observables that do not change sign if the trajectories are observed backward in time. We find…
Various notions of fluctuations exist depending on the way one chooses to measure them. We discuss two extreme cases (continuous measurement versus long inter-measurement times) and we see their relation with entropy production and with…
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…
In systems removed from equilibrium, intrinsic microscopic fluctuations become correlated over distances comparable to the characteristic macroscopic length over which the external constraint is exerted. In order to investigate this…
This paper addresses the question of the fluctuations of the empirical entropy of a chain of infinite order. We assume that the chain takes values on a finite alphabet and loses memory exponentially fast. We consider two possible…