# Quantum Thermodynamics in the Refined Weak Coupling Limit

## TL;DR

This paper develops a thermodynamic framework for quantum systems in the refined weak coupling limit, accounting for non-Markovian dynamics and external drivings, and redefines internal energy accordingly.

## Contribution

It introduces a novel thermodynamic approach for the refined weak coupling limit, incorporating non-Markovian effects and external drivings in quantum thermodynamics.

## Key findings

- Derived first and second laws in the refined weak coupling regime.
- Extended the framework to include external drivings.
- Reconsidered the definition of internal energy in this context.

## Abstract

We present a thermodynamic framework for the refined weak coupling limit. In this limit the interaction between system and environment is weak, but not negligible. As a result, the system dynamics becomes non-Markovian breaking divisibility conditions. Nevertheless, we propose a derivation of the first and second law just in terms of the reduced system dynamics. To this end, we extend the refined weak coupling limit for allowing slowly-varying external drivings, and reconsider the definition of internal energy due to the non-negligible interaction.