# Equilibration on average in quantum processes with finite temporal resolution

## TL;DR

This paper investigates when multi-time quantum processes with limited temporal resolution can be approximated by equilibrium processes, extending the concept of equilibration on average to multiple times and providing bounds on distinguishability.

## Contribution

It generalizes the notion of equilibration on average to multi-time processes with finite temporal resolution and establishes bounds on their distinguishability from equilibrium.

## Key findings

- Derived conditions for multi-time equilibration with finite temporal resolution
- Established an upper bound on a distinguishability measure between processes
- Identified multi-time contributions depending on temporal resolution and observer disturbance

## Abstract

We characterize the conditions under which a multi-time quantum process with a finite temporal resolution can be approximately described by an equilibrium one. By providing a generalization of the notion of equilibration on average, where a system remains closed to a fixed equilibrium for most times, to one which can be operationally assessed at multiple times, we place an upper-bound on a new observable distinguishability measure comparing a multi-time process with a finite temporal resolution against a fixed equilibrium one. While the same conditions on single-time equilibration, such as a large occupation of energy levels in the initial state remain necessary, we obtain genuine multi-time contributions depending on the temporal resolution of the process and the amount of disturbance of the observer's operations on it.