Nonextensive distribution and factorization of the joint probability

Abstract

The problem of factorization of a nonextensive probability distribution is discussed. It is shown that the correlation energy between the correlated subsystems in the canonical composite system can not be neglected even in the thermodynamic limit. In consequence, the factorization approximation should be employed carefully according to different systems. It is also shown that the zeroth law of thermodynamics can be established within the framework of the Incomplete Statistical Mechanics (ISM ).

Nonextensive statistics and incomplete information

“…Very recently, a possible alternative theoretical basis for T DF was proposed [2,20]. The new formalism is based on a reflection about the conditions of physical application of the standard probability theory which is sometimes referred to as Kolmogorov probability theory [21].…”

Incomplete nonextensive statistics and the zeroth law of thermodynamics

“…Introduction. Incomplete statistics (IS) proposed by Wang [1] and Tsallis' statistics [2,3] have been two important branches of nonextensive statistical mechanics [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently, IS has been used to research the thermostatistic properties of a variety of physical systems with long-range interacting and/or long-duration memory and many significant results have been obtained [6][7][8][9][10][11][12][13][14][15][16].…”

“…Incomplete statistics (IS) proposed by Wang [1] and Tsallis' statistics [2,3] have been two important branches of nonextensive statistical mechanics [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently, IS has been used to research the thermostatistic properties of a variety of physical systems with long-range interacting and/or long-duration memory and many significant results have been obtained [6][7][8][9][10][11][12][13][14][15][16]. For example, it has been found that for some chaotic systems evolving in fractal phase space [7,8], the entropy change in time due to the fractal geometry is assimilated to the information growth through the scale refinement; and that the generalized fermion distributions based on incomplete information hypothesis can be useful for describing correlated electron systems [9,10].…”

Two generalizations of the Boltzmann equation

“…Non-extensive thermodynamics has been developed in the past two decades as a statistical theory to deal with such physical stationary states [4,5,6]. Initially based on mathematical investigations of a generalized definition of Boltzmann's entropy, a never-decreasing macroscopical state-parameter intimately connected to statistical probabilities of microstates, this theory soon started to study dynamicses possibly leading to such states.…”