Local quantum thermal susceptibility

TL;DR

This paper introduces the local quantum thermal susceptibility, a measure of the maximum precision in temperature estimation through local measurements, linking quantum estimation theory with thermodynamics and phase transition detection.

Contribution

It presents a novel quantifier for local thermal response in quantum systems, bridging quantum estimation theory with thermodynamics and phase transition analysis.

Findings

Quantifies the best achievable accuracy for local temperature estimation.

Highlights the role of ground state distinguishability at low temperatures.

Provides a method to locate quantum phase transitions.

Abstract

Thermodynamics relies on the possibility to describe systems composed of a large number of constituents in terms of few macroscopic variables. Its foundations are rooted into the paradigm of statistical mechanics, where thermal properties originate from averaging procedures which smoothen out local details. While undoubtedly successful, elegant and formally correct, this approach carries over an operational problem: what is the precision at which such variables are inferred, when technical/practical limitations restrict our capabilities to local probing? Here we introduce the local quantum thermal susceptibility, a quantifier for the best achievable accuracy for temperature estimation via local measurements. Our method relies on basic concepts of quantum estimation theory, providing an operative strategy to address the local thermal response of arbitrary quantum systems at equilibrium. At low temperatures it highlights the local distinguishability of the ground state from the excited sub-manifolds, thus providing a method to locate quantum phase transitions.