New version of quantum mechanics at finite temperatures as a ground for description of nearly perfect fluids

TL;DR

This paper introduces a generalized quantum mechanics framework at finite temperatures, called $(, k)$-dynamics, to better describe nearly perfect fluids and modify thermodynamics using a new macroparameter, the effective action.

Contribution

It proposes a novel microdescription of quantum systems at finite temperatures incorporating vacuum effects, introducing the Schroedingerian operator and the effective action as key concepts.

Findings

Effective action relates to internal energy, temperature, and entropy.

New macroparameters improve description of nearly perfect fluids.

Modified thermodynamics based on temperature-dependent wave functions.

Abstract

We suggest a more general than quantum statistical mechanics ($QSM$) microdescription of objects in a heat bath taken into account a vacuum as an object environment - modification of quantum mechanics at finite temperatures; we call it $(\hbar, k)$-dynamics ($ \hbar kD$). This approach allows us in a new manner to calculate some important macroparameters and to modify standard thermodynamics. We create an effective apparatus for features description of nearly perfect fluids in various mediums. As an essentially new model of an object environment we suppose a quantum heat bath and its properties, including cases of cold and warm vacuums, are studied. We describe the thermal equilibrium state in place of the traditional density operator in term of a wave function the amplitude and phase of which have temperature dependence. We introduce a new generative operator, Schroedingerian, or stochastic action operator, and show its fundamental role in the microdescription. We demonstrate that a new macroparameter, namely the effective action, can be obtained through averaging of the Schroedingerian over the temperature dependent wave function. It is established that such different parameters as internal energy, effective temperature, and effective entropy and their fluctuations can be expressed through a single quantity - the effective action.