Abstract
A representation theorem for the entropy functional of a system of an arbitrary but finite number of particles is proved. This theorem is a generalization of the main result of a previous paper of ours [J. Math. Phys. 16, 1453 (1975)], which gives a characterization of the entropy functional on the set of all probability densities f on Rn s.t. flogf is integrable. As may be expected when n is a random variable, the expression for entropy consists of two parts; one which arises from the ignorance about n and another which is the average, over n, of the conditional entropy given the number of particles. As in the above‐mentioned paper, the expression includes the term corresponding to chemical reactions (with n replaced by the average number of particles) and the continuous analog of the Hartley entropy. It is conjectured that this last term might be of some significance in physics.
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