Auxiliary Variables in Statistical Mechanics: Variational Principle

1968 ◽  
Vol 9 (12) ◽  
pp. 2109-2120
Author(s):  
Gerald Speisman
Keyword(s):  
Variational Principle ◽  
Statistical Mechanics ◽  
Auxiliary Variables

scholarly journals Communication: Maximum caliber is a general variational principle for nonequilibrium statistical mechanics

2015 ◽  
Vol 143 (5) ◽  
pp. 051104 ◽  
Author(s):  
Michael J. Hazoglou ◽  
Valentin Walther ◽  
Purushottam D. Dixit ◽  
Ken A. Dill
Keyword(s):  
Variational Principle ◽  
Statistical Mechanics ◽  
Nonequilibrium Statistical Mechanics

scholarly journals Entropy production at weak Gibbs measures and a generalized variational principle

2009 ◽  
Vol 29 (4) ◽  
pp. 1327-1347 ◽  
Author(s):  
MICHIKO YURI
Keyword(s):  
Variational Principle ◽  
Statistical Mechanics ◽  
Entropy Production ◽  
Invariant Measures ◽  
Stationary Process ◽  
Gibbs Measures ◽  
Generalized Variational Principle ◽  
Probability Measures ◽  
Equilibrium Statistical Mechanics ◽  
Non Equilibrium

AbstractWe consider piecewise invertible systems exhibiting intermittency and establish a generalized variational principle adapted to a non-stationary process in the following sense; the supremum is attained by non-singular (not necessarily invariant) probability measures and if the system exhibits hyperbolicity, then it reduces to the usual variational principle for the pressure. Our method relies on Ruelle’s program in the study of non-equilibrium statistical mechanics to analyze dissipative phenomena. We show non-positivity of entropy production at weak Gibbs measures and clarify when it indeed vanishes. We also discuss a generalized variational principle in the context of σ-finite invariant measures.

Sign in / Sign up

Export Citation Format

Share Document