The Time Evolution of Entropy Production in Nonlinear Dynamic Systems

Abstract

General characteristics of entropy production in a fluid system are investigated from a thermodynamic viewpoint. A basic expression for entropy production due to irreversible transport of heat or momentum is formulated together with balance equations of energy and momentum in a fluid system. It is shown that entropy production always decreases with time when the system is of a pure diffusion type without advection of heat or momentum. The minimum entropy production (MinEP) property is thus intrinsic to a pure diffusion-type system. However, this MinEP property disappears when the system is subject to advection of heat or momentum due to dynamic motion. When the rate of advection exceeds the rate of diffusion of heat or momentum, entropy production tends to increase over time. The maximum entropy production (MaxEP), suggested as a selection principle for steady states of nonlinear non-equilibrium systems, can therefore be understood as a characteristic feature of systems with dynamic instability. The observed mean state of vertical convection of the atmosphere is consistent with the condition for MaxEP presented in this study.