Models of Finite Bath and Generalised Thermodynamics

Abstract

We consider the approach of a sample system in contact with a heat bath environment, to arrive at equilibrium distributions for the energies of the sample system. In canonical ensemble, we assume the size of the bath to be infinite. The real baths or environments are expected to have a finite size. Different conditions on the bath properties yield different equilibirum distributions of the sample system. Explicitly, the gaussian ensemble and q-exponential distributions are discussed. The various thermodynamic quantities like entropy and free energy are nonadditive in these formalisms. We also present a new model which can be seen as an intermediate case of the above two scenarios. The connection between noadditivity in these models with the deformed numbers in the context of q-analysis is also highlighted.