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Entropy in nonequilibrium statistical mechanics is investigated theoretically so as to extend the well-established equilibrium framework to open nonequilibrium systems. We first derive a microscopic expression of nonequilibrium entropy for…
In equilibrium, the fluctuation-dissipation theorem (FDT) expresses the response of an observable to a small perturbation by a correlation function of this variable with another one that is conjugate to the perturbation with respect to…
We extend the definition of non-adiabatic entropy production given for Markovian systems in [M. Esposito and C. Van den Broeck, Phys. Rev. Lett. 104 090601, (2010)], to arbitrary non-Markov ergodic dynamics. We also introduce a notion of…
Boltzmann's principle is used to select the "most probable" realization (macrostate) of an isolated or closed thermodynamic system, containing a small number of particles ($N \llsp \infty$), for both classical and quantum statistics. The…
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…
We prove a transient fluctuation theorem for the currents for continuous-time Markov jump processes with stationary rates, generalizing an asymptotic result by Andrieux and Gaspard [J. Stat. Phys. 127, 107 (2007)] to finite times. The…
We demonstrate that the Gibbs-Shannon entropy is applicable to non-equilibrium systems of any size and boundary conditions. The change in microscopic entropy can be attributed to the stochastic nature of dynamic processes and to the…
For chemical reaction networks described by a master equation, we define energy and entropy on a stochastic trajectory and develop a consistent nonequilibrium thermodynamic description along a single stochastic trajectory of reaction…
A large number of processes in the mesoscopic world occur out of equilibrium, where the time course of a system evolution becomes immensely important since it is driven principally by dissipative effects. Non-equilibrium steady states…
We propose a thermodynamically consistent minimal model to study synchronization which is made of driven and interacting three-state units. This system exhibits at the mean-field level two bifurcations separating three dynamical phases: a…
This monograph attempts a theory of every 'thing' that can be distinguished from other things in a statistical sense. The ensuing statistical independencies, mediated by Markov blankets, speak to a recursive composition of ensembles (of…
Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic…
Based on a recent progress in nonequilibrium statistical mechanics of infinitely extended quantum systems, a nonequlibrium steady state (NESS) is constructed for a single-level quantum dot interacting with two free reservoirs under less…
We discuss the validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits. Both the minimum and the maximum entropy production principle are understood within dynamical fluctuation theory.…
We collect recent results on deriving useful response relations also for nonequilibrium systems. The approach is based on dynamical ensembles, determined by an action on trajectory space. (Anti)Symmetry under time-reversal separates two…
The "ratchet principle" asserts that non-equilibrium systems which violate parity symmetry generically exhibit steady-state currents. As recently shown, there are exceptions to this principle, due to the existence of hidden time-reversal…
Thermodynamics is based on the notions of energy and entropy. While energy is the elementary quantity governing physical dynamics, entropy is the fundamental concept in information theory. In this work, starting from first principles, we…
Fluctuation theorems are a generalization of thermodynamics on small scales and provide the tools to characterize the fluctuations of thermodynamic quantities in non-equilibrium nanoscale systems. They are particularly important for…
The most rigorous physical description of non-equilibrium gas dynamics is rooted in the numerical solution of the Boltzmann equation. Yet, the large number of degrees of freedom and the wide range of both spatial and temporal scales render…
We build a rigorous nonequilibrium thermodynamic description for open chemical reaction networks of elementary reactions. Their dynamics is described by deterministic rate equations satisfying mass action law. Our most general framework…