A Theoretical Basis for Maximum Entropy Production

Abstract

Maximum entropy production (MaxEP) is a conjectured selection criterionfor the stationary states of non-equilibrium systems. In the absenceof a firm theoretical basis, MaxEP has largely been applied in anad hoc manner. Consequently its apparent successes remain somethingof a curiosity while the interpretation of its apparent failuresis fraught with ambiguity. Here we show how Jaynes’ maximum entropy(MaxEnt) formulation of statistical mechanics provides a theoreticalbasis for MaxEP which answers two outstanding questions that haveso far hampered its wider application: What do the apparent successesand failures of MaxEP actually mean physically? And what is the appropriateentropy production that is maximized in any given problem? As illustrativeexamples, we show how MaxEnt underpins previous applications of MaxEPto planetary climates and fluid turbulence. We also discuss the relationshipof MaxEP to the fluctuation theorem and Ziegler’s maximum dissipationprinciple.