Temporal extensivity of Tsallis' entropy and the bound on entropy production rate

Details Temporal extensivity of Tsallis' entropy and the bound on entropy production rate Temporal extensivity of Tsallis' entropy and the bound on entropy production rate

2006-03-21

arxiv.org/abs/cond-mat/0603550v1

Physics

Condensed Matter

Statistical Mechanics

25 pages, no figures

Scientific paper

10.1103/PhysRevE.74.021120

The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation for the Tsallis entropy. They are primarily concerned with nonlinear dynamical systems at the edge of chaos. Here, it is shown by generalizing a formulation of thermostatistics based on time averages recently proposed by Carati [A. Carati, Physica A 348, 110 (2005)] that, whenever relevant, the Tsallis entropy indexed by $q$ is temporally extensive: linear growth in time, i.e., finite entropy production rate. Then, the universal bound on the entropy production rate is shown to be $1/|1-q|$ . The property of the associated probabilistic process, i.e., the sojourn time distribution, determining randomness of motion in phase space is also analyzed.

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