A quantum generalization of equilibrium statistical thermodynamics: Effective macroparameters

We propose a generalization of statistical thermodynamics in which quantum effects are taken into account on the macrolevel without explicitly using the operator formalism while traditional relations between the macroparameters are preserved. In a generalized thermostat model, thermal equilibrium is characterized by an effective temperature bounded from below. We introduce fundamental theoretical macroparameters: the effective entropy and the effective action. Because the effective entropy is nonzero at low temperatures, we can write the third law of thermodynamics in the form postulated by Nernst. The effective action at any temperature coincides with the product of standard deviations of the coordinate and momentum in the Heisenberg uncertainty relation and is therefore bounded from below. We establish that the ratio of the effective action to the effective entropy in the low-temperature limit is determined by a holistic stochastic-action constant depending on the Planck and Boltzmann constants. We show that the same results can be obtained in the framework of a modified version of thermofield dynamics in which the quantum oscillator is described by a temperature-dependent complex macroscopic wave function. We study the discrepancy between the behavior of the action-to-entropy ratio in the low-temperature limit in our proposed theory and that in quantum equilibrium statistical mechanics, which can be verified experimentally.