Probability current and thermodynamics of open quantum systems

TL;DR

This paper generalizes the probability current concept to finite-dimensional quantum systems, including open systems, and investigates its properties and relation to thermodynamic quantities like heat and work.

Contribution

It introduces a unified definition of probability current applicable to both isolated and open quantum systems, linking it to thermodynamic concepts.

Findings

Probability current is well-defined for finite-dimensional quantum systems.

The generalized current relates to thermodynamic heat and work in open systems.

Properties of the probability current are characterized and analyzed.

Abstract

This paper explores the generalization of the concept of a "probability current", familiar from wave-function quantum mechanics, to quantum systems with finite-dimensional Hilbert spaces. The generalized definition applies both to isolated systems evolving via the Schr\"odinger equation and to more general open systems obeying the Lindblad master equation. We establish several properties of the probability current and explore its relation to thermodynamic heat and work.