  This is an analysis of the additivity of the entropy of thermodynamical
systems with finite heat baths. It is presented an expression for the physical
entropy of weakly interacting ergodic systems, and it is shown that it is valid
for both the microcanonical (constant energy), the Boltzmann-Gibbs canonical
(infinite heat bath) and the Tsallis (finite heat bath) ensembles. This
physical entropy may be written as a variant of Tsallis entropy. 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.
