Entropy production in bulk isothermal relaxation

Four theorems relating to complete monotonicity of entropy production in isothermal bulk relaxation have been proved, and in another two cases, it is shown by numerical experiment that the entropy production is probably monotonic also. The total entropy and the total energy do not in general relax with the same rate constant, and under many conditions the time constant for entropy relaxation approaches twice the time constant for energy relaxation. We speculate that the maximum entropy principle used in the information-theoretic approach to bulk relaxation may be synonymous with the principle of complete monotonicity of entropy production.