Quantum analysis and thermodynamic operator relations in stochastic energetics

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.

Poisson bracket operator

“…For other applications of quantum analysis, see, for example, Refs. [11][12][13][14][15][16] Let us consider an operator f ( A) where f (x) is a smooth function of x. Then the Gâteaux differential of this operator is defined by [3] df…”