Irreversibility, Loschmidt echo, and thermodynamic uncertainty relation

TL;DR

This paper establishes a fundamental link between irreversibility, Loschmidt echo, and thermodynamic uncertainty in quantum Markov processes, unifying classical and quantum perspectives on thermodynamic precision limits.

Contribution

It introduces a new bound on measurement precision based on Loschmidt echo, connecting irreversibility with thermodynamic uncertainty in quantum dynamics.

Findings

Precision is bounded by Loschmidt echo, reflecting irreversibility.

Derivation of thermodynamic uncertainty relations from the bound.

Unified framework for classical and quantum thermodynamic uncertainty.

Abstract

Entropy production characterizes irreversibility. This viewpoint allows us to consider the thermodynamic uncertainty relation, which states that a higher precision can be achieved at the cost of higher entropy production, as a relation between precision and irreversibility. Considering the original and perturbed dynamics, we show that the precision of an arbitrary counting observable in continuous measurement of quantum Markov processes is bounded from below by Loschmidt echo between the two dynamics, representing the irreversibility of quantum dynamics. When considering particular perturbed dynamics, our relation leads to several thermodynamic uncertainty relations, indicating that our relation provides a unified perspective on classical and quantum thermodynamic uncertainty relations.