Thermodynamic Limit in Statistical Physics

Abstract

The thermodynamic limit in statistical thermodynamics of many-particle systems is an important but often overlooked issue in the various applied studies of condensed matter physics. To settle this issue, we review tersely the past and present disposition of thermodynamic limiting procedure in the structure of the contemporary statistical mechanics and our current understanding of this problem. We pick out the ingenious approach by N. N. Bogoliubov, who developed a general formalism for establishing of the limiting distribution functions in the form of formal series in powers of the density. In that study he outlined the method of justification of the thermodynamic limit when he derived the generalized Boltzmann equations. To enrich and to weave our discussion, we take this opportunity to give a brief survey of the closely related problems, such as the equipartition of energy and the equivalence and nonequivalence of statistical ensembles. The validity of the equipartition of energy permits one to decide what are the boundaries of applicability of statistical mechanics. The major aim of this work is to provide a better qualitative understanding of the physical significance of the thermodynamic limit in modern statistical physics of the infinite and "small" many-particle systems.

28 pages, Refs.180. arXiv admin note: text overlap with arXiv:1011.2981, arXiv:0812.0943 by other authors

References in corpus (5)

• The large deviation approach to statistical mechanics
• Generalized canonical ensembles and ensemble equivalence
• The generalized canonical ensemble and its universal equivalence with the microcanonical ensemble
• Theory of Transport Processes and the Method of the Nonequilibrium Statistical Operator
• Thermostats, chaos and Onsager reciprocity

Cited by in corpus (11)

• Gibbs, Boltzmann, and negative temperatures
• Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems
• Exact derivation of a finite-size-scaling law and corrections to scaling in the geometric Galton-Watson process
• Thermodynamics of quantum photon spheres
• The Interplay of Finite and Infinite Size Stability in Quadratic Bosonic Lindbladians
• Statistical mechanics of two-dimensional foams: Physical foundations of the model
• Thermodynamics of bosonic systems in adS spacetime
• Boundary conditions and electromagnetic effects on the phase transition of a zero spin bosonic system
• Core-Halo Quasi-Stationary States in the Hamiltonian Mean-Field Model
• Weyl conjecture and thermal radiation of finite systems
• Approaching the Thermodynamic Limit of an Ideal Gas