Statistical Mechanics: A Short Treatise
This book presents a critical and modern analysis of the conceptual foundations of statistical mechanics as laid down in Boltzmann's works. The author emphasizes the relation between microscopic reversibility and macroscopic irreversibility. Students will find a clear and detailed explanation of fundamental concepts such as equipartition, entropy, and ergodicity. They will learn about Brownian motion, the modern treatment of the thermodynamic limit phase transitions, the microscopic and macroscopic theory of the coexistence of phases, statistical mechanics of stationary states, and fluctuations and dissipation in chaotic motions.
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analysis Anosov map Anosov system average kinetic energy average value Boltzmann Boltzmann's equation boundary conditions Brownian motion called cellules chaotic hypothesis Chap classical statistical mechanics collisions computed consider constant correlation functions corresponding defined degrees of freedom denote density derivatives described dimension dynamics elements entropy equation equilibrium equivalence ergodic hypothesis evolution fact finite fixed fluctuation theorem formula free energy Gaussian given grand canonical ensemble hard core Hence implies integral interaction Ising model lattice magnetization Markov partition mathematical means microcanonical ensemble microscopic model of thermodynamics momentum number of particles observable orthodic ensembles parameters partition function permutation phase space cells phase transitions physical possible pressure probability distribution problem properties quantities quantum remark respect reversible sense sequence simple solution spin configuration SRB distribution stationary statistical ensembles surface symmetry T-particles temperature theory thermodynamic limit tions trajectory variables vectors velocity virial volume zero