Microscopic and macroscopic perspectives on stationary nonequilibrium states

Abstract

The main subject of the thesis is the study of stationary nonequilibrium states trough the use of microscopic stochastic models that encode the physical interaction in the rules of Markovian dynamics for particles configurations. These models are known as interacting particles systems and are simple enough to be treated analytically but also complex enough to capture essential physical behaviours. The thesis is organized in two parts. The part 1 is devoted to the microscopic theory of the stationary states. We characterize these states developing some general structures that have an interest in themselves. In this part there is an interlude dedicated to discrete calculus on discrete manifolds with an exposition a little bit different to the one available in literature and some original definitions. The part 2 studies the problem macroscopically. In particular we consider the large deviations asymptotic behavior for a class of solvable one dimensional models of heat conduction. Both part 1 and 2 begin with an introduction of motivational character followed by an overview of the relevant results and a summary explaining the organization. Even tough the two parts are strictly connected they can be read independently after chapter 1. The material is presented in such a way to be self-consistent as much as possible.

arXiv commentPhD thesis, awarded by SISSA at GSSI (2017)

References in corpus (20)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Fluctuations in Stationary non Equilibrium States
• Large Deviation of the Density Profile in the Steady State of the Open Symmetric Simple Exclusion Process
• Steady-state selection in driven diffusive systems with open boundaries
• Stochastic interacting particle systems out of equilibrium
• Exact Free Energy Functional for a Driven Diffusive Open Stationary Nonequilibrium System
• Large deviation functional of the weakly asymmetric exclusion process
• Nonequilibrium and irreversibility
• Lagrangian phase transitions in nonequilibrium thermodynamic systems
• Onsager reciprocity relations without microscopic reversibility
• Acceleration of convergence to equilibrium in Markov chains by breaking detailed balance
• A diffusive system driven by a battery or by a smoothly varying field
• Stationary non-equilibrium properties for a heat conduction model
• Variational calculation of transport coefficients in diffusive lattice gases
• A quasi-potential for conservation laws with boundary conditions
• Strong asymmetric limit of the quasi-potential of the boundary driven weakly asymmetric exclusion process
• Static large deviations of boundary driven exclusion processes
• Rates for irreversible Gibbsian Ising models
• Which random walks are cyclic?