A selection of nonequilibrium issues

Abstract

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 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.

Lecture notes from the 5th Prague Summer School on Mathematical Statistical Mechanics (2006), 55 pages

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Cited by in corpus (18)

• Macroscopic fluctuation theory
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Direct measurement of nonequilibrium system entropy is consistent with Gibbs-Shannon form
• Large deviation approach to nonequilibrium systems
• Non-equilibrium steady states : maximization of the Shannon entropy associated to the distribution of dynamical trajectories in the presence of constraints
• Computation of current cumulants for small nonequilibrium systems
• Martingales for physicists: A treatise on stochastic thermodynamics and beyond
• Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
• Territorial Developments Based on Graffiti: a Statistical Mechanics Approach
• Reflection Positivity for Parafermions
• Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q
• The KPZ equation in a half space with flat initial condition and the unbinding of a directed polymer from an attractive wall
• Pointwise estimates and exponential laws in metastable systems via coupling methods
• On quenched and annealed critical curves of random pinning model with finite range correlations
• Interacting Fermions Picture for Dimer Models
• Phase transition in ferromagnetic Ising model with a cell-board external field
• Percolation transition for random forests in $d\ge 3$
• A note on the non-commutative Laplace-Varadhan integral lemma