Statistical mechanics of “negative temperature” states

The Meaning of Temperature and Entropy in Classical Statistical Mechanics

This paper began life as a serious attempt to understand the classical foundations of thermodynamics, but ended up doing crazy things like defining the temperature and entropy of single molecules. Nevertheless, there is method behind the madness, because in terms of these generalized definitions I am able to prove that the generalized notion of temperature reduces to the standard notion under c...

Statistical mechanics of time independent nondissipative nonequilibrium states.

We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent nondissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming that the phase space may be divided into time independent, locally ergodic domains, we argue that within such domains the relative probabilities of microstates are g...

Effective-temperature concept: a physical application for nonextensive statistical mechanics.

The H-theorem [(df/dt) ≤ 0] for a free-energy functional, f = u-θs (with u and s representing, respectively, the internal energy and a generalized entropy of a given physical system), has been proven previously by making use of a nonlinear Fokker-Planck equation. Herein we focus on a nonlinear Fokker-Planck equation derived by means of a coarse-graining procedure on the equations of motion of a...

Statistical Mechanics

Statistical Mechanics

where pi ≡ p(x = i). If only M of the K states have non-zero probability and that probability is 1/M then S = logM . In this special case the entropy is the log of the number of occupied states. An analog of this special case in the continuous domain occurs in Liouville’s Theorem. This states that if the volume of phase space (i.e. of the x variable, but now multivariate and continuous) is some...