Classical Statistical Mechanics

2015 ◽  
pp. 111-168
Author(s):  
Isamu Kusaka
Keyword(s):  
Statistical Mechanics ◽  
Classical Statistical Mechanics

Measurement in quantum mechanics and classical statistical mechanics

1992 ◽  
Vol 167 (4) ◽  
pp. 319-325 ◽  
Author(s):  
Marcello Cini ◽  
Maurizio Serva
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Classical Statistical Mechanics

scholarly journals On the Geometrical Representation of Classical Statistical Mechanics

2018 ◽  
Author(s):  
Georgios C. Boulougouris
Keyword(s):  
Statistical Mechanics ◽  
Parametric Representation ◽  
Gauss Map ◽  
Inner Product ◽  
Necessary And Sufficient Condition ◽  
Thermodynamic State ◽  
Classical Statistical Mechanics ◽  
Geometrical Representation ◽  
Definition Of ◽  
Necessary And Sufficient

In this work a geometrical representation of equilibrium and near equilibrium statistical mechanics is proposed. Using a formalism consistent with the Bra-Ket notation and the definition of inner product as a Lebasque integral, we describe the macroscopic equilibrium states in classical statistical mechanics by “properly transformed probability Euclidian vectors” that point on a manifold of spherical symmetry. Furthermore, any macroscopic thermodynamic state “close” to equilibrium is described by a triplet that represent the “infinitesimal volume” of the points, the Euclidian probability vector at equilibrium that points on a hypersphere of equilibrium thermodynamic state and a Euclidian vector a vector on the tangent bundle of the hypersphere. The necessary and sufficient condition for such representation is expressed as an invertibility condition on the proposed transformation. Finally, the relation of the proposed geometric representation, to similar approaches introduced under the context of differential geometry, information geometry, and finally the Ruppeiner and the Weinhold geometries, is discussed. It turns out that in the case of thermodynamic equilibrium, the proposed representation can be considered as a Gauss map of a parametric representation of statistical mechanics.

Asymptotic Equivalence of Equilibrium Ensembles of Classical Statistical Mechanics

1971 ◽  
Vol 12 (6) ◽  
pp. 933-935 ◽  
Author(s):  
Luigi Galgani ◽  
Luciano Manzoni ◽  
Antonio Scotti
Keyword(s):  
Statistical Mechanics ◽  
Asymptotic Equivalence ◽  
Classical Statistical Mechanics
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