# Role of work in matter exchange between finite quantum systems

## TL;DR

This paper explores how quantum systems exchange heat and particles, revealing deviations from classical transport laws due to work done during contact, with implications for understanding quantum thermodynamics.

## Contribution

It introduces a transport matrix for quantum systems that can be asymmetric and non-positive, extending classical transport theory to quantum regimes.

## Key findings

- Transport matrix can be asymmetric and non-positive in quantum systems.
- Spontaneous transport occurs without temperature or chemical potential differences.
- Standard transport laws are recovered in the large-system or long-time limits.

## Abstract

Close to equilibrium, the exchange of particles and heat between macroscopic systems at different temperatures and different chemical potentials is known to be governed by a matrix of transport coefficients which is positive and symmetric. We investigate the amounts of heat and particles that are exchanged between two small quantum systems within a given time, and find them characterized by a transport matrix which neither needs to be symmetric nor positive. At larger times even spontaneous transport can be observed in the total absence of temperature and chemical potential differences provided that the two systems are different in size. All these deviations from standard transport behavior can be attributed to the fact that work is done on the system in the processes contacting and separating those parts of the system that initially possess different temperatures and chemical potentials. The standard transport properties are recovered for vanishing work and also in the limit of large systems and sufficiently large contact times. The general results are illustrated by an example.