Thermodynamics and Statistical Mechanics of a Three-Level Maser

Abstract

The three "spin" states of a maser are treated as individual chemical species. It is assumed that these three species are in thermal equilibrium with the lattice at temperature $T$ but that they are not necessarily in chemical equilibrium with one another. The principle of minimum entropy production is used to derive an equation of reaction equilibrium from which the steady-state behavior of the system with a microwave pump may be completely described. In addition to the population distribution, which is in agreement in first order with the results obtained by solving the rate equations, explicit expressions are obtained for the internal energy, heat capacity, and entropy. The calculations are extended to include spontaneous emission and cross-relaxation as well as the usual thermal relaxation mechanisms.