Quantum Analysis and Thermodynamic Operator Relations in Stochastic Energetics

TL;DR

This paper develops a quantum model of Brownian motion coupled with a classical bath, defining a heat operator that obeys thermodynamic-like relations, bridging quantum analysis with stochastic energetics.

Contribution

It introduces a quantum Brownian motion model with a heat operator satisfying thermodynamic relations, extending stochastic energetics into the quantum domain.

Findings

The heat operator satisfies relations analogous to thermodynamic laws.

The model links quantum analysis with stochastic energetics.

Provides a framework for quantum thermodynamic operator relations.

Abstract

We introduce a model of the quantum Brownian motion coupled to a classical neat bath by using the operator differential proposed in the quantum analysis. We then define the heat operator by adapting the idea of the stochastic energetics. The introduced operator satisfies the relations which are analogous to the first and second laws of thermodynamics.