Quantum Statistical Mechanics. IV. Non-Equilibrium Probability Operator and Stochastic, Dissipative Schrodinger Equation

TL;DR

This paper derives a probability operator for non-equilibrium quantum systems and introduces a stochastic, dissipative Schrödinger equation, linking dissipative propagators with thermodynamic forces via the fluctuation-dissipation theorem.

Contribution

It presents a novel derivation of the non-equilibrium probability operator and the associated stochastic Schrödinger equation, connecting thermodynamics with quantum dynamics.

Findings

Derived the non-equilibrium probability operator.

Formulated the stochastic, dissipative Schrödinger equation.

Linked propagators through the fluctuation-dissipation theorem.

Abstract

The probability operator for a generic non-equilibrium quantum system is derived. The corresponding stochastic, dissipative Schr\"odinger equation is also given. The dissipative and stochastic propagators are linked by the fluctuation-dissipation theorem that is derived from the unitary condition on the time propagator. The dissipative propagator is derived from thermodynamic force and entropy fluctuation operators that are in general non-linear.