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Rényi entropies and observables.

Bernhard Lesche¹

¹Departamento de Física, Universidade Federal de Juiz de Fora, Juiz de Fora MG, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 25, 2004

Summary

Rényi entropies in macroscopic thermodynamic systems cannot be linked to observables, even when defined by microstate probabilities. This study clarifies the concept of an observable in this context.

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Area of Science:

Thermodynamics
Statistical Mechanics
Information Theory

Background:

Macroscopic thermodynamic systems are often described using probabilities of microstates.
Rényi entropies are a generalization of Shannon entropy used in information theory and statistical mechanics.

Purpose of the Study:

To investigate the relationship between Rényi entropies and observables in macroscopic thermodynamic systems.
To clarify the definition and role of observables in this context.

Main Methods:

Theoretical analysis of Rényi entropies based on microstate probabilities.
Conceptual clarification of the term 'observable' within thermodynamic frameworks.

Main Results:

Rényi entropies, when defined via microstate probabilities, cannot be directly related to physical observables.
The study provides a refined understanding of what constitutes an observable in thermodynamics.

Conclusions:

The direct link between Rényi entropies and observables in macroscopic systems is not supported by current definitions.
A clearer definition of observables is crucial for advancing the understanding of thermodynamic properties and information measures.

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