Methods of Contemporary Mathematical Statistical Physics

2006/10/31 by Marek Biskup, C. Maes, K. Netocny +7
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Class (philosophy) #Computer science #Epistemology #Ising model #Lattice (music) #Library science #Markov Chains and Monte Carlo Methods #Mathematics #Philosophy #Physics #Potts model #Property (philosophy) #Reflection (computer programming) #Statistical Mechanics and Entropy #Statistical mechanics #Statistical physics #Subject (documents) #Theoretical physics #cond-mat.stat-mech #math-ph #math.MP #math.PR #msc:60G50 #msc:82B20 #msc:82B26

paper · pdf · doi:10.1007/978-3-540-92796-9

published as Lect. Notes Math. 1970 (2009) 247 - 306 · Lecture notes from the 5th Prague Summer School on Mathematical Statistical Mechanics (2006), 55 pages

arxiv created 2007/01/16 · openalex publication_date 2009/01/01 · arxiv updated 2009/12/01 · openalex created_date 2017/04/07 · openalex updated_date 2026/08/05

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.

Citations

• Boltzmann Entropy for Dense Fluids Not in Local Equilibrium
• On the absence of spontaneous symmetry breaking and of crystalline ordering in two-dimensional systems
• Ferromagnetism in the Hubbard Model: A Constructive Approach
• On the symmetry of the Gibbs states in two dimensional lattice systems
• Orbital Ordering in Transition-Metal Compounds: I. The 120-Degree Model
• On the (Boltzmann) entropy of non-equilibrium systems
• Absence of breakdown of continuous symmetry in two-dimensional models of statistical physics
• General Theory of Spin-Wave Interactions
• On the critical behavior of the magnetization in high-dimensional Ising models
• The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas
• Gibbs vs Boltzmann Entropies
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Infrared bounds, phase transitions and continuous symmetry breaking
• Ordering, metastability and phase transitions in two-dimensional systems
• Rigorous Analysis of Discontinuous Phase Transitions via Mean-Field Bounds
• Orbital order in classical models of transition-metal compounds
• Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States
• Time-Reversal and Entropy
• The continuous spin random field model: Ferromagnetic ordering in d>=3
• Axioms for Euclidean Green's functions