A basic problem in the correlations between statistics and thermodynamics

Abstract

By using a fonctionelle of probability distributions, several different statistical physics including extensive and nonextensive statistics are unified in a general method. The essential equivalence between the MaxEnt process of the most probable probility distribution in these statistics and the famous thermodynamical relation dU TdS = is strictly proved without any additional assumption. Moreover, itis expounded that all the conclusions of these different statistics can be directly derived from the equivalent relation.

Inherent correlations between thermodynamics and statistical physics in extensive and nonextensive systems

“…(21) and Eqs. (4b) and (15), one can derive the probability distribution of a system satisfying Tsallis' statistics as [6,8]…”

“…( 13) and ( 15), one can maximize the entropy of a system which is subjected to some constraint conditions. When there is not any work exchange between the system and the surroundings, the objective function may be given by [6]…”

“…Equation ( 16) has been used to calculate the probability distribution when the entropy attains its maximum value under the given temperature condition [4][5][6][7][8][9][10]. It is significant to note that when there does not exist the work exchange between the system and the surroundings, it is equivalent to take the internal energy U of the system as one constraint condition and choose the heat exchange Q between the system and the surroundings as the other constraint condition.…”

“…How are they connected by some basic relations? This is a very fundamental problem, which has received increasing attention [4][5][6]. In this paper, the correlations between the different statistical physics including extensive and nonextensive [7][8][9][10][11][12][13][14][15][16][17] statistics and thermodynamics will be investigated by a unified method and some very general conclusions will be obtained.…”