On the Problem of the Entropy of the Universe as a Whole

Abstract

The well-known problem of the entropy of the universe as a whole arises from the difficulties encountered by classical thermodynamics---first in failing to account for the presumed fact that the entropy of the universe has always been increasing at an enormous rate and nevertheless has not yet reached its maximum value---and second in failing to allow an emotionally satisfactory feeling towards our universe whose ultimate fate would be the stagnation of "heat-death." The purpose of the present article is to examine this problem from the point of view of the extension of thermodynamics to general relativity which has previously been made by the author.A number of earlier contributions to the solution of the problem, which have been made from the standpoint of classical thermodynamics or statistical mechanics, are first briefly described in order to emphasize the very different character of the contribution to the problem made in the present article. It is then pointed out that the problem of the entropy of the universe arises in the classical thermodynamics because of the presumption that thermodynamic processes cannot take place both reversibly and at a finite rate, and that the general nature of the contribution to the problem offered by relativistic thermodynamics consists in showing the possibility of thermodynamic changes which could take place at a finite rate and at the same time reversibly without increase in entropy.The principles of relativistic thermodynamics are th…