Non Linear Kinetics underlying Generalized Statistics

Details Non Linear Kinetics underlying Generalized Statistics Non Linear Kinetics underlying Generalized Statistics

2001-03-22

arxiv.org/abs/cond-mat/0103467v4

Physica A 296, 405 (2001)

Physics

Condensed Matter

Statistical Mechanics

31 pages, no figures

Scientific paper

10.1016/S0378-4371(01)00184-4

The purpose of the present effort is threefold. Firstly, it is shown that there exists a principle, that we call Kinetical Interaction Principle (KIP), underlying the non linear kinetics in particle systems, independently on the picture (Kramers, Boltzmann) used to describe their time evolution. Secondly, the KIP imposes the form of the generalized entropy associated to the system and permits to obtain the particle statistical distribution, both as stationary solution of the non linear evolution equation and as the state which maximizes the generalized entropy. Thirdly, the KIP allows, on one hand, to treat all the classical or quantum statistical distributions already known in the literature in a unifying scheme and, on the other hand, suggests how we can introduce naturally new distributions. Finally, as a working example of the approach to the non linear kinetics here presented, a new non extensive statistics is constructed and studied starting from a one-parameter deformation of the exponential function holding the relation $f(-x)f(x)=1$.

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