Temporal extensivity of Tsallis' entropy and the bound on entropy production rate
Sumiyoshi Abe, Yutaka Nakada (Institute of Physics, University of, Tsukuba, Japan)

TL;DR
This paper demonstrates that Tsallis' entropy can be temporally extensive with a finite production rate and establishes a universal bound on this rate, contributing to the understanding of nonextensive statistical mechanics.
Contribution
It generalizes a thermostatistics formulation to show Tsallis entropy's temporal extensivity and derives a universal entropy production rate bound.
Findings
Tsallis entropy is linearly extensive over time for relevant systems.
The universal bound on entropy production rate is 1/|1-q|.
Analysis of sojourn time distribution relates to phase space randomness.
Abstract
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 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 . 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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