Affinity-based extension of non-extensive entropy and statistical mechanics

Keisuke Okamura

Physica A: Statistical Mechanics and its Applications, 2020, vol. 557, issue C

Abstract: Tsallis’ non-extensive entropy is extended to incorporate the dependence on affinities between the microstates of a system. At the core of our construction of the extended entropy (H) is the concept of the effective number of dissimilar states, termed the ‘effective diversity’ (Δ). It is a unique integrated measure derived from the probability distribution among states and the affinities between states. The effective diversity is related to the extended entropy through the Boltzmann’s-equation-like relation, H=lnqΔ, in terms of the Tsallis’ q-logarithm. A new principle called the Nesting Principle is established, stating that the effective diversity remains invariant under arbitrary grouping of the constituent states. It is shown that this invariance property holds only for q=2; however, the invariance is recovered for general q in the zero-affinity limit (i.e. the Tsallis and Boltzmann–Gibbs case). Using the affinity-based extended Tsallis entropy, the microcanonical and the canonical ensembles are constructed in the presence of general between-state affinities. It is shown that the classic postulate of equal a priori probabilities no longer holds but is modified by affinity-dependent terms. As an illustration, a two-level system is investigated by the extended canonical method, which manifests that the thermal behaviour of the thermodynamic quantities at equilibrium are affected by the between-state affinity. Furthermore, some applications and implications of the affinity-based extended diversity/entropy for information theory and biodiversity theory are addressed in appendices.

Keywords: Tsallis entropy; Non-extensive statistical mechanics; Effective diversity; Affinity-based extension; Nesting-invariance (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437120304404
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:557:y:2020:i:c:s0378437120304404

DOI: 10.1016/j.physa.2020.124849

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().