Comparison of Entropy Production Rates in Two Different Types of Self-organized Flows: B\'{e}nard Convection and Zonal flow

TL;DR

This paper explores the duality between minimum and maximum entropy production principles in self-organized flows, using thermodynamic potentials and bifurcation analysis to explain phenomena like H-mode in fusion plasma.

Contribution

It introduces a dual relation between minimum and maximum EPR principles via Legendre transformation and generalizes Onsager's dissipation function for nonlinear regimes.

Findings

Duality between minimum and maximum EPR principles established

Bifurcation and hysteresis explained through thermodynamic potential analysis

EPR can be either minimized or maximized depending on system driving conditions

Abstract

Entropy production rate (EPR) is often effective to describe how a structure is self-organized in a nonequilibrium thermodynamic system. The "minimum EPR principle" is widely applicable to characterizing self-organized structures, but is sometimes disproved by observations of "maximum EPR states." Here we delineate a dual relation between the minimum and maximum principles; the mathematical representation of the duality is given by a Legendre transformation. For explicit formulation, we consider heat transport in the boundary layer of fusion plasma [Phys. Plasmas {\bf 15}, 032307 (2008)]. The mechanism of bifurcation and hysteresis (which are the determining characteristics of the so-called H-mode, a self-organized state of reduced thermal conduction) is explained by multiple tangent lines to a pleated graph of an appropriate thermodynamic potential. In the nonlinear regime, we have to generalize Onsager's dissipation function. The generalized function is no longer equivalent to EPR; then EPR ceases to be the determinant of the operating point, and may take either minimum or maximum values depending on how the system is driven.