# Thermodynamic utility of Non-Markovianity from the perspective of resource interconversion

## TL;DR

This paper explores the relationship between non-Markovianity and thermodynamic resource interconversion, showing that non-Markovian dynamics are necessary for resource backflow in quantum thermodynamics.

## Contribution

It characterizes Lindblad operators for unital and thermal operations and links non-Markovianity with entropy production and free energy dynamics.

## Key findings

- Non-Markovianity correlates with negative entropy production rates.
- Lindblad operators for unital and thermal operations are fully characterized.
- Non-Markovianity is necessary for resource backflow like purity and free energy.

## Abstract

We establish a connection between non-Markovianity and negative entropy production rate for various classes of quantum operations. We analyse several aspects of unital and thermal operations in connection with resource theories of purity and thermodynamics. We fully characterize Lindblad operators corresponding to unital operations. We also characterize the Lindblad dynamics for a large class of thermal operations. We next generalize the definition of the entropy production rate for the non-equilibrium case to connect it with the rate of change of free energy of the system, and establish complementary relations between non-Markovianity and maximum loss of free energy. We naturally conclude that non-Markovianity in terms of divisibility breaking is a necessary resource for the backflow of other resources like purity or free energy under the corresponding allowed operations.