Microscopic interpretation of generalized entropy

Generalized entropy, that has been recently proposed, puts all the known and apparently different entropies like The Tsallis, the Renyi, the Barrow, the Kaniadakis, the Sharma-Mittal and the loop quantum gravity entropy within a single umbrella. However, the microscopic origin of such generalized entropy as well as its relation to thermodynamic system(s) is not clear. In the present work, we will provide a microscopic thermodynamic explanation of generalized entropy(ies) from canonical and grand-canonical ensembles. It turns out that in both the canonical and grand-canonical descriptions, the generalized entropies can be interpreted as the statistical ensemble average of a series of microscopic quantity(ies) given by various powers of (-kln rho)(n) (with n being a positive integer and rho symbolizes the phase space density of the respective ensemble), along with a term representing the fluctuation of Hamiltonian and number of particles of the system under consideration (in case of canonical ensemble, the fluctuation on the particle number vanishes).

Automated summary

This study introduces the concept of generalized entropy and investigates its microscopic origin and its relation to thermodynamic systems. The results show that generalized entropy can be interpreted as the statistical average of a series of microscopic quantities using canonical and grand-canonical ensembles.