# Thermodynamics of weakly coherent collisional models

## TL;DR

This paper introduces weakly coherent collisional models where environmental elements have approximate thermal states with quantum coherence, leading to modified thermodynamic laws and resource bounds that enable heat-to-energy conversion without work.

## Contribution

It formulates a new class of collisional models incorporating quantum coherence, extending thermodynamics beyond purely thermal systems with a resource-based perspective.

## Key findings

- Quantum coherence acts as a resource in thermodynamics.
- Modified first and second laws include coherence contributions.
- Coherence can be consumed to convert heat into ordered energy.

## Abstract

We introduce the idea of weakly coherent collisional models, where the elements of an environment interacting with a system of interest are prepared in states that are approximately thermal, but have an amount of coherence proportional to a short system-environment interaction time in a scenario akin to well-known collisional models. We show that, in the continuous-time limit, the model allows for a clear formulation of the first and second laws of thermodynamics, which are modified to include a non-trivial contribution related to quantum coherence. Remarkably, we derive a bound showing that the degree of such coherence in the state of the elements of the environment represents a resource, which can be consumed to convert heat into an ordered (unitary-like) energy term in the system, even though no work is performed in the global dynamics. Our results therefore represent an instance where thermodynamics can be extended beyond thermal systems, opening the way for combining classical and quantum resources.