# Full counting statistics approach to the quantum non-equilibrium Landauer bound

## TL;DR

This paper develops a full counting statistics framework for dissipated heat to analyze Landauer's principle, deriving bounds on heat dissipation and linking them to dynamical phase transitions in quantum systems.

## Contribution

It introduces a general family of bounds on dissipated heat using full counting statistics and connects these bounds to dynamical phase transitions in quantum non-equilibrium systems.

## Key findings

- Derived bounds on mean dissipated heat from a quantum system.
- Linked the bounds to the non-unitality of system dynamics.
- Applied the framework to a three-level quantum system with thermal environment.

## Abstract

We develop the full counting statistics of dissipated heat to explore the relation with Landauer's principle. Combining the two-time measurement protocol for the reconstruction of the statistics of heat with the minimal set of assumptions for Landauer's principle to hold, we derive a general one-parameter family of upper and lower bounds on the mean dissipated heat from a system to its environment. Furthermore, we establish a connection with the degree of non-unitality of the system's dynamics and show that, if a large deviation function exists as stationary limit of the above cumulant generating function, then our family of lower and upper bounds can be used to witness and understand first-order dynamical phase transitions. For the purpose of demonstration, we apply these bounds to an externally pumped three level system coupled to a finite sized thermal environment.