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

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 $q$ 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.