Article (Scientific journals)
Rényi Entropy in Statistical Mechanics
Fuentes, Jesús; Goncalves, Jorge
2022In Entropy, 24 (8), p. 1080
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Keywords :
statistical mechanics; Rényi entropy; Helmholtz free energy; relative free energy; non-equilibrium thermodynamics
Abstract :
[en] Rényi entropy was originally introduced in the field of information theory as a parametric relaxation of Shannon (in physics, Boltzmann–Gibbs) entropy. This has also fuelled different attempts to generalise statistical mechanics, although mostly skipping the physical arguments behind this entropy and instead tending to introduce it artificially. However, as we will show, modifications to the theory of statistical mechanics are needless to see how Rényi entropy automatically arises as the average rate of change of free energy over an ensemble at different temperatures. Moreover, this notion is extended by considering distributions for isospectral, non-isothermal processes, resulting in relative versions of free energy, in which the Kullback–Leibler divergence or the relative version of Rényi entropy appear within the structure of the corrections to free energy. These generalisa- tions of free energy recover the ordinary thermodynamic potential whenever isothermal processes are considered.
Research center :
- Luxembourg Centre for Systems Biomedicine (LCSB): Systems Control (Goncalves Group)
Disciplines :
Physics
Author, co-author :
Fuentes, Jesús ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > Systems Control
Goncalves, Jorge ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > Systems Control
External co-authors :
yes
Language :
English
Title :
Rényi Entropy in Statistical Mechanics
Publication date :
05 August 2022
Journal title :
Entropy
ISSN :
1099-4300
Publisher :
Multidisciplinary Digital Publishing Institute (MDPI), Basel, Switzerland
Special issue title :
Rényi Entropy: Sixty Years Later
Volume :
24
Issue :
8
Pages :
1080
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Physics and Materials Science
FnR Project :
FNR14609071 - Patient-specific Dynamical Modeling And Optimization Of Deep Brain Stimulation, 2020 (01/09/2021-31/08/2024) - Jorge Gonçalves
Funders :
FNR - Fonds National de la Recherche [LU]
Available on ORBilu :
since 22 August 2022

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