# Almost thermal operations: inhomogeneous reservoirs

## TL;DR

This paper explores how small inhomogeneities in reservoirs affect thermodynamic operations, revealing that such deviations can significantly alter work generation and the interpretation of second laws in resource theories.

## Contribution

It introduces models of inhomogeneous reservoirs in thermal operations and analyzes their impact on state transformations and thermodynamic properties.

## Key findings

- Inhomogeneities can produce the same channels as homogeneous reservoirs for small deviations.
- Thermodynamics differ notably when considering work extraction and second law interpretations.
- Models show that even mild deviations can lead to different thermodynamic behaviors.

## Abstract

The resource theory of thermal operations explains the state transformations that are possible in a very specific thermodynamic setting: there is only one thermal bath, auxiliary systems can only be in corresponding thermal state (free states), and the interaction must commute with the free Hamiltonian (free operation). In this paper we study the mildest deviation: the reservoir particles are subject to inhomogeneities, either in the local temperature (introducing resource states) or in the local Hamiltonian (generating a resource operation). For small inhomogeneities, the two models generate the same channel and thus the same state transformations. However, their thermodynamics is significantly different when it comes to work generation or to the interpretation of the "second laws of thermal operations".