Quantum mechanical analogue of the zeroth law of thermodynamics. (On the problem of incorporating Thermodynamics into Quantum Theory)

TL;DR

This paper explores integrating the zeroth law of thermodynamics into quantum theory by using the Schrödinger uncertainty relation, enabling comparison of vacuum states and advancing stochastic thermodynamics in quantum systems.

Contribution

It introduces a method to explicitly incorporate the zeroth law of thermodynamics into quantum theory via the Schrödinger uncertainty relation, comparing vacuum states and previous approaches.

Findings

Comparison of squeezed coherent states and correlated coherent states.

Analysis of stochastic thermodynamics within quantum vacuum states.

Evaluation against previous thermodynamic quantum models.

Abstract

This approach to the incorporation of stochastic thermodynamics into quantum theory is based on the conception of consistent inclusion of the holistic stochastic environmental influence described by wave functions of the arbitrary vacuum, which was proposed in our paper previously. In this study, we implement the possibility of explicitly incorporating the zeroth law of stochastic thermodynamics in the form of the saturated Schr\"odinger uncertainty relation into quantum theory. This allows comparatively analyzing the sets of states of arbitrary vacuums, namely, squeezed coherent states (SCSs) and correlated coherent states (CCSs). In addition, we compare the results of the construction of stochastic thermodynamics using SCSs and TCCSs with the versions involving the incorporation of thermodynamics into quantum theory developed previously and based on thermofield dynamics and quantum statistical mechanics.