Abstract
The thermodynamic properties of the laser distribution in the steadily oscillating state are investigated to determine the minimum characteristic of the entropy production. First, the laser Langevin equation for five random variables is treated in the light of the stochastic calculus to deduce the photon-number rate equationn = − C+(n − nc) + [A/(1 + sn)](n−nA), where nn and n4 are the two constants of the fluctuation attributed to the noise forces subject to the usual fluctuation-dissipation theorem, withn 4 < 0 for the inverted atomic population. We then combine the dynamics of the lasing mode with a model open system of the Lebowitz type with two reservoirs for which the entropy productionσ(p) is expressed and made subject to a variational principle: The modified variation scheme, the same as Prigogine's local potential method, is shown to give the exact lasing distributionp as the optimum between two distributions of thermal type with temperatures far from each other.
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Hasegawa, H., Nakagomi, T. Semiclassical laser theory in the stochastic and thermodynamic frameworks. J Stat Phys 21, 191–214 (1979). https://doi.org/10.1007/BF01008698
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DOI: https://doi.org/10.1007/BF01008698