The Physical Meaning of the Rényi Relative Entropy

Özet

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.