This paper reviews various applications of the theory of smooth dynamical systems to
conceptual problems of nonequilibrium statistical mecanics. We adopt a new point of view …

The purpose of this book is to present various results and techniques from the theory of
stochastic processes and in particular diffusion processes that are useful in the study of …

We extend the work of Kurchan on the Gallavotti–Cohen fluctuation theorem, which yields a
symmetry property of the large deviation function, to general Markov processes. These …

These lecture notes give a short review of methods such as the matrix ansatz, the additivity
principle or the macroscopic fluctuation theory, developed recently in the theory of non …

We analyze the microscopic evolution of a system undergoing a far-from-equilibrium
thermodynamic process. Explicitly accounting for the degrees of freedom of participating …

We present a selective overview of the current state of our knowledge (more precisely of our
ignorance) regarding the derivation of Fourier's Law, J (r)=− κ∇ T (r); J the heat flux, T the …

We introduce a numerical procedure to evaluate directly the probabilities of large deviations
of physical quantities, such as current or density, that are local in time. The large-deviation …

The title of this book already says something about its contents and historical origin, but
since it is meant in a rigorous mathematical context, a few words of explanation may be …

A concept of time-reversed entropy per unit time is introduced in analogy with the entropy
per unit time by Shannon, Kolmogorov, and Sinai. This time-reversed entropy per unit time …

The aim of the present interdisciplinary review is to carry out a comparative analysis of the
notions of thermodynamic entropy, information entropy and entropy of non-equilibrium states …