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Entropy Optimization, Generalized Logarithms, and Duality Relations.

Angel R Plastino1, Constantino Tsallis2,3,4, Roseli S Wedemann5

  • 1CeBio y Departamento de Ciencias Básicas, Universidad Nacional del Noroeste de la Província de Buenos Aires, UNNOBA, CONICET, Roque Saenz Peña 456, Junin B6000, Argentina.

Entropy (Basel, Switzerland)
|December 23, 2022
PubMed
Summary
This summary is machine-generated.

This study explores power-law entropies (Sq) in thermostatistics, focusing on the duality between q-logarithm and q-exponential functions. It investigates entropic functionals and their associated duality relations for broader applications.

Keywords:
Sq entropiesduality relationsentropy optimizationgeneralized entropiesgeneralized logarithms

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Area of Science:

  • Statistical Mechanics
  • Non-extensive Thermodynamics

Background:

  • Generalizations of Boltzmann-Gibbs thermostatistics using non-standard entropies are an active research area.
  • Power-law, non-additive entropies (Sq) have shown numerous successful applications.

Purpose of the Study:

  • To analyze the structural features of Sq thermostatistics.
  • To investigate the duality relation between the q-logarithm and q-exponential functions.
  • To explore entropic functionals and their corresponding duality relations.

Main Methods:

  • Analysis of the q-logarithm function (lnqx).
  • Investigation of duality relations.
  • Examination of entropic functionals.

Main Results:

  • The q-logarithm function associated with Sq entropy exhibits a duality relation with the q-exponential function.
  • This duality links to maximum-entropy probability distributions.

Conclusions:

  • The structural features of Sq thermostatistics, particularly the q-logarithm/q-exponential duality, are significant.
  • Further investigation into entropic functionals and their dualities can extend the applicability of these non-standard thermostatistics.