Abstract :
This is an analysis of the thermodynamical entropy of systems with finite heat baths and of its additivity. It is presented an expression for the physical entropy of weakly interacting ergodic systems, and it is shown how it relates to the traditional entropies of the micro-canonical (constant energy), the canonical Boltzmann–Gibbs (infinite heat bath) and the Tsallis (finite heat bath) ensembles. This physical entropy contains one term that is a variant of the Tsallis entropy, and it becomes an additive function after a suitable choice of additive constants, in a procedure reminiscent to the solution presented by Gibbs to the paradox bearing his name.
