Thermodynamic Steady States in Simple Electrical Circuits

Abstract

Electrical circuits provide good examples of systems which gravitate towards the three possible thermodynamic conditions of equilibrium, metastability or dissipative steady state. Circuits are driven towards any one of the three conditions simply by increasing total entropy or decreasing available energy. The thermodynamic condition for steady state conduction in a number of simple LCR and hot filament circuits is found to be 1/(ds_tot/dψ) = 0 or 1/(de_avail/dψ) = 0 where s_tot and e_avail are the total entropy and available energy of the system and its surroundings, and ψ is any single valued variable which describes the condition or state of the total system. This is the inverse of the equilibrium and metastable conditions. It holds for all systems examined, whereas the Onsager-Prigogine principle, ds_tot/dt = 0 at steady state, holds only in one case. This shows that the principle is not the causative principle of the steady state. As expected, the analysis also demonstrates that electric circuit theory is fully consistent with the second law of thermodynamics as well as with the first.