# Thermodynamics of Quantum Information Flows

## TL;DR

This paper extends thermodynamic principles to open quantum systems, deriving inequalities that bound power output and incorporate information effects, with applications to quantum information processing and Maxwell demon models.

## Contribution

It introduces nonequilibrium free energy inequalities and local thermodynamic bounds for quantum subsystems, highlighting the role of information in quantum thermodynamics.

## Key findings

- Derived a nonequilibrium free energy inequality for quantum systems.
- Established local Clausius and free energy inequalities with information contributions.
- Applied the theory to analyze an autonomous Maxwell demon.

## Abstract

We report two results complementing the second law of thermodynamics for Markovian open quantum systems coupled to multiple reservoirs with different temperatures and chemical potentials. First, we derive a nonequilibrium free energy inequality providing an upper bound for a maximum power output, which for systems with inhomogeneous temperature is not equivalent to the Clausius inequality. Secondly, we derive local Clausius and free energy inequalities for subsystems of a composite system. These inequalities differ from the total system one by the presence of an information-related contribution and build the ground for thermodynamics of quantum information processing. Our theory is used to study an autonomous Maxwell demon.