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Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived…
The influence of dissipation on the fluctuation statistics of the total energy is investigated through both a phenomenological and a stochastic model for dissipative energy-transfer through a cascade of states. In equilibrium the states…
Non-equilibrium stochastic dynamics of several active Brownian systems are modeled in terms of non-linear velocity dependent force. In general, this force may consist of both even and odd functions of velocity. We derive the expression for…
Understanding the physics of non-equilibrium systems remains as one of the major open questions in statistical physics. This problem can be partially handled by investigating macroscopic fluctuations of key magnitudes that characterise the…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
The time-reversal symmetry of nonequilibrium fluctuations is experimentally investigated in two out-of-equilibrium systems namely, a Brownian particle in a trap moving at constant speed and an electric circuit with an imposed mean current.…
Active systems are characterized by a continuous production of entropy at steady state. We study the statistics of entropy production within a lattice-based model of interacting active particles that is capable of motility-induced phase…
There are two main approaches to non-equlibrium statistical mechanics: one using stochastic processes and the other using dynamical systems. To model the dynamics during inflation one usually adopts a stochastic description, which is known…
Motivated by stochastic models of climate phenomena, the steady-state of a linear stochastic model with additive Gaussian white noise is studied. Fluctuation theorems for nonequilibrium steady-states provide a constraint on the character of…
A positive rate of entropy production at steady state is a distinctive feature of truly non-equilibrium processes. Exact results, while being often limited to simple models, offer a unique opportunity to explore the thermodynamic features…
For stochastic non-equilibrium dynamics like a Langevin equation for a colloidal particle or a master equation for discrete states, entropy production along a single trajectory is studied. It involves both genuine particle entropy and…
We revisit the model of a Brownian particle in a heat bath submitted to an actively controlled force proportional to the velocity that leads to thermal noise reduction (cold damping). We investigate the influence of the continuous feedback…
The total entropy production and its three constituent components are described both as fluctuating trajectory-dependent quantities and as averaged contributions in the context of the continuous Markovian dynamics, described by stochastic…
The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of…
These notes give a summary of techniques used in large deviation theory to study the fluctuations of time-additive quantities, called dynamical observables, defined in the context of Langevin-type equations, which model equilibrium and…
We present a method of estimating the rate of entropy production in underdamped dynamics by decomposing it into contributions originating in different non-equilibrium effects. Specifically, a non-zero average velocity, a non-thermal width…
The emergence of non-gaussian distributions for macroscopic quantities in nonequilibrium steady states is discussed with emphasis on the effective criticality and on the ensuing universality of distribution functions. The following problems…
This paper addresses fundamental aspects of statistical mechanics such as the motivation of a classical state space with spontaneous transitions, the meaning of non-equilibrium in the context of thermalization, and the justification of…
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…
The fluctuations of macroscopic observables in quantum systems which are in a nonequilibrium steady state are studied rigorously in the thermodynamic limit. In particular, the nonequilibrium steady state (NESS) of a quantum spin system that…