Phenomenological Non-Equilibrium Quantum Thermodynamics based on Modified von Neumann Equations

TL;DR

This paper proposes a modified von Neumann equation framework to incorporate irreversibility in quantum thermodynamics, especially for decomposed systems with interacting sub-systems, extending traditional reversible quantum mechanics.

Contribution

It introduces a novel modification of von Neumann equations for sub-systems, enabling the modeling of irreversibility in quantum thermodynamics with interactions through partitions.

Findings

Modified equations produce irreversibility in decomposed systems

Framework extends quantum mechanics to include thermodynamic behavior

Interaction through partitions is effectively modeled

Abstract

The wide-spread opinion is that original quantum mechanics is a reversible theory, but this statement is only true for undecomposed systems, that are those systems which sub-systems are out of consideration. Taking sub-systems into account, as it is by definition necessary for decomposed systems, the interaction Hamiltonians which are absent in undecomposed systems generate irreversibility. Thus, the following two-stage task arises: How to modify von Neumann's equation for undecomposed systems so that irreversibility appears, and how this modification affects decomposed systems ? The first step was already done and is repeated below, whereas the second step to formulate a quantum thermodynamics of decomposed systems is performed here by modifying the von Neumann equations of the sub-systems by a procedure wich is similar to that of Lindblad's equation, but different because the sub-systems interact with one another through partitions.