Modeling Electric Discharges with Entropy Production Rate Principles

Thomas Christen

doi:10.3390/e11041042

Abstract

Under which circumstances are variational principles based on entropy production rate useful tools for modeling steady states of electric (gas) discharge systems far from equilibrium? It is first shown how various different approaches, as Steenbeck’s minimum voltage and Prigogine’s minimum entropy production rate principles are related to the maximum entropy production rate principle (MEPP). Secondly, three typical examples are discussed, which provide a certain insight in the structure of the models that are candidates for MEPP application. It is then thirdly argued that MEPP, although not being an exact physical law, may provide reasonable model parameter estimates, provided the constraints contain the relevant (nonlinear) physical effects and the parameters to be determined are related to disregarded weak constraints that affect mainly global entropy production. Finally, it is additionally conjectured that a further reason for the success of MEPP in certain far from equilibrium systems might be based on a hidden linearity of the underlying kinetic equation(s).

Highlights

Electric discharges appear in various natural phenomena like lightning, St
The believe is that the maximum entropy production (MEP) state gives a “best” or “most unbiased” estimate on the basis of the available information, which is contained in the model (the choice of z, the expression for Ṡ(z), and the constraints, like balance equations etc.)
An illuminating example is given by Rebhan [22], who compares the exact shock front solution in an ideal gas with maximum entropy production rate principle (MEPP) solutions for all cases, where one of the three hydrodynamic balance equations for mass, momentum, and energy, is disregarded

Summary

Introduction

Electric (gas) discharges appear in various natural phenomena like lightning, St. Elmo’s fire, and spark discharges. Another possible application of MEPP to torch arcs might be to model electrode spots with the Steenbeck principle in order to obtain anode or even cathode spot voltage drop (cf [2]). According to Section 2., the maximum and minimum entropy production rate (or power dissipation) principles for steady states are equivalent.

Results

Conclusion