Abstract
The Boltzmann-Gibbs relative entropy provides the difference between the off-equilibrium and equilibrium free energy terms associated with Boltzmann-Gibbs entropy. In this work, we studied whether this physical meaning can be given to R\'{e}nyi relative entropy definition. We find that this is possible only in the limit as $q$ approaches to 1. This shows that R\'{e}nyi relative entropy has a physical meaning only when the system can already be explained by ordinary Boltzmann-Gibbs entropy. We also note that this result is independent of the internal energy constraint employed.
Highlights
Rényi entropy has been introduced by A
The relative entropy acts as a generalized free energy in the ordinary thermostatistical framework when one makes use of the associated equilibrium distribution as the reference distribution
In this Letter, we investigated whether Rényi relative entropy can play the role of a generalized free energy in a thermostatistical framework
Summary
Rényi entropy has been introduced by A. Second issue regarding the importance of the concept of relative entropy is that ordinary BG entropy cannot be generalized to continuum rigorously just by changing summation to integration since it fails to be invariant under different parametrizations It will not be bounded neither from below nor above (see Ref.[10] and references therein). All of the remarks above can be summarized by the statement that the concept of relative entropy is a generalization of the corresponding entropy definition both in terms of probability distributions and continuum case. It is our aim in this paper to present some results related to the definition of Rényi relative entropy concerning its physical meaning and relation to internal energy constraints.
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