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Ehrenfest urns with interaction that are connected in a ring is considered as a paradigm model for non-equilibrium thermodynamics and is shown to exhibit two distinct non-equilibrium steady states (NESS) of uniform and non-uniform particle…
Non-equilibrium processes in Schottky systems generate by projection onto the equilibrium subspace reversible accompanying processes for which the non-equilibrium variables are functions of the equilibrium ones. The embedding theorem which…
We consider a purely harmonic chain of oscillators which is perturbed by a stochastic noise. Under this perturbation, the system exhibits two conserved quantities: the volume and the energy. At the level of the hydrodynamic limit, under…
We analyze the non-equilibrium steady states (NESS) of a one dimensional harmonic chain of $N$ atoms with alternating masses connected to heat reservoirs at unequal temperatures. We find that the temperature profile defined through the…
Fluctuation relations for the entropy production in non equilibrium stationary states of Ising models are investigated by Monte Carlo simulations. Systems in contact with heat baths at two different temperatures or subject to external…
We consider stationary driven systems in contact with a thermal equilibrium bath. There is a constant (Joule) heat dissipated from the steady system to the environment as long as all parameters are unchanged. As a natural generalization…
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…
We present a scenario for the nonequilibrium dynamics in the limit of small entropy production. We discuss (i) the appearence of different time-scales, (ii) the modification of the fluctuation-dissipation theorem and its relation to…
The dynamics of irreversible relaxation of non-equilibrium macroscopic systems is discussed. Arguments are developed showing that the general process is supported by two independent successive mechanisms. One is mixing and it follows pure…
Motivated by compartmental analysis in engineering and biophysical systems, we present a variational framework for the nonequilibrium thermodynamics of systems involving both distributed and discrete (finite dimensional) subsystems by…
We present the results of analytical and numerical studies of a one-dimensional nonlocal and nonlinear diffusion equation describing non-equilibrium processes ranging from aggregation phenomena to cooperation of individuals. We study a…
We discuss differential-- versus integral--equation based methods describing out--of thermal equilibrium systems and emphasize the importance of a well defined reduction to statistical observables. Applying the projection operator approach,…
We study thermalization and non-equilibrium dynamics in a dissipative quantum many-body system -- a chain of ions with two points of the chain driven by thermal bath under different temperature. Instead of a simple linear temperature…
Ability of dynamical systems to relax to equilibrium has been investigated since the invention of statistical mechanics, which establishes the connection between dynamics of many-body Hamiltonian systems and phenomenological thermodynamics.…
A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this review we summarize recent theoretical advances along these lines.…
We investigate transport in several translationally invariant spin-1/2 chains in the limit of high temperatures. We concretely consider spin transport in the anisotropic Heisenberg chain, the pure Heisenberg chain within an alternating…
Despite its intrinsic non-equilibrium origin, thermoelectricity in nanoscale systems is usually described within a static scattering approach which disregards the dynamical interaction with the thermal baths that maintain energy flow. Using…
We study the model of a strongly non-linear chain of particles coupled to two heat baths at different temperatures. Our main result is the existence and uniqueness of a stationary state at all temperatures. This result extends those of…
It is shown that the structure of non-equilibrium thermodynamic system far from equilibrium can be captured in terms of a generalized "Nambu dynamics", in the presence of fluctuation effects in non-equilibrium thermodynamics. Triangular…
With focus on anharmonic chains, we develop a nonlinear version of fluctuating hydrodynamics, in which the Euler currents are kept to second order in the deviations from equilibrium and dissipation plus noise are added. The required…