Mathematical theory of nonequilibrium steady states pdf

This is in contrast with the behavior of approximate Lyapunov functions based on entropy production that when driven far from equilibrium often keep exhibiting temporal oscillations even close to stationarity.

A selection of nonequilibrium issues more. We give a pedagogical introduction to a selection of recently discussed topics in nonequilibrium statistical mechanics, concentrating mostly on formal structures and on general principles.

Part I contains an overview of the formalism of Part I contains an overview of the formalism of lattice gases that we use to explain various symmetries and inequalities generally valid for nonequilibrium systems, including the fluctuation symmetry, Jarzynski equality, and the direction of currents. In Part II we concentrate on the macroscopic state and how entropy provides a bridge between microscopic dynamics and macroscopic irreversibility; included is a construction of quantum macroscopic states and a result on the equivalence of ensembles.

Incoherent boundary conditions and metastates more. Steady state statistics of driven diffusions more. Mathematical Physics and Quantum Physics. H-theorems from autonomous equations more.

Abstract: The H-theorem is an extension of the Second Law to a time-sequence of states that need not be equilibrium ones. In this paper we review and we rigorously establish the connection with macroscopic autonomy. If for a Hamiltonian If for a Hamiltonian dynamics for many particles, the Publisher: arxiv. On and beyond entropy production: the case of Markov jump processes more.

Abstract: How is it that entropy derivatives almost in their own are characterizing the state of a system close to equilibrium, and what happens further away from it? We explain within the framework of Markov jump processes why We explain within the framework of Markov jump processes why fluctuation theory can be based on Heat conduction networks more.

We study networks of interacting oscillators, driven at the boundary by heat baths at possibly different temperatures. A set of first elementary questions are discussed concerning the uniqueness of a stationary possibly Gibbsian density A set of first elementary questions are discussed concerning the uniqueness of a stationary possibly Gibbsian density and the nature of the entropy Time-Reversal and Entropy more.

There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations We explain on an elementary mathematical level the relations between entropy production, phase-space contraction and time-reversal starting from a deterministic dynamics. Skip to search form Skip to main content Skip to account menu You are currently offline.

Some features of the site may not work correctly. DOI: Meerson , P. Sasorov , A. View PDF on arXiv. Save to Library Save. Create Alert Alert.

Share This Paper. Figures from this paper. Citation Type. Has PDF. Publication Type. Journal of Statistical Physics. Dynamical ensembles have been introduced to study constrained stochastic processes. In the microcanonical ensemble, the value of a dynamical observable is constrained to a given value. In the … Expand. Statistical optimization for passive scalar transport: maximum entropy production vs.

We derive rigorous results on the link between the principle of maximum entropy production 7 and the principle of maximum KolmogorovSinai entropy for a Markov model of the passive scalar 8 diffusion … Expand.

View 1 excerpt, cites background. Thermal contact is the archetype of non-equilibrium processes driven by constant nonequilibrium constraints enforced by reservoirs exchanging conserved microscopic quantities. At a mesoscopic scale … Expand. Perspective: Maximum caliber is a general variational principle for dynamical systems. The Journal of chemical physics. Stochastic thermodynamics, fluctuation theorems and molecular machines.

Reports on progress in physics. Physical Society. Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport. It vanishes if and only if the stationary system is reversible and in equilibrium.

Moreover, in the cases of Markov chains and diffusion processes on manifolds, it can be expressed in terms of circulations on directed cycles. Regarding entropy production fluctuations, the Gallavotti-Cohen fluctuation theorem is rigorously proved.