Renormalization and Statistical Mechanics in Many-Particle Systems. I. Hamiltonian Perturbation Method

1966 ◽  
Vol 152 (1) ◽  
pp. 247-260 ◽  
Author(s):  
Duane C. Wallace
Keyword(s):  
Statistical Mechanics ◽  
Perturbation Method ◽  
Particle Systems ◽  
Hamiltonian Perturbation

scholarly journals A diagrammatic analysis of the variational perturbation method for classical fluids

Soft Matter ◽  
2018 ◽  
Vol 14 (23) ◽  
pp. 4721-4734 ◽  
Author(s):  
Leo Lue
Keyword(s):  
Statistical Mechanics ◽  
Perturbation Method ◽  
Classical Fluids ◽  
Diagrammatic Analysis ◽  
Variational Perturbation ◽  
Field Perspective

The statistical mechanics of classical fluids can be approached from the particle perspective, where the focus is on the positions of the particles, or from the field perspective, where the focus is on the form of the interaction fields generated by the particles. These two perspectives can be combined through the variational perturbation method.

scholarly journals THERMODYNAMIC LIMIT IN STATISTICAL PHYSICS

2014 ◽  
Vol 28 (09) ◽  
pp. 1430004 ◽  
Author(s):  
A. L. KUZEMSKY
Keyword(s):  
Statistical Mechanics ◽  
Thermodynamic Limit ◽  
Statistical Physics ◽  
Formal Series ◽  
Distribution Functions ◽  
Particle Systems ◽  
Boltzmann Equations ◽  
Qualitative Understanding ◽  
Statistical Ensembles ◽  
Equipartition Of Energy

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 Bogoliubov, who developed a general formalism for establishing 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.

Statistical Mechanics of Hard‐Particle Systems

1968 ◽  
Vol 48 (7) ◽  
pp. 3139-3155 ◽  
Author(s):  
Emmanuel Meeron ◽  
Arnold J. F. Siegert
Keyword(s):  
Statistical Mechanics ◽  
Particle Systems ◽  
Hard Particle
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