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, namely determining 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.
Highlights
Thermodynamics relies on the possibility to describe systems composed of a large number of constituents in terms of few macroscopic variables
We have proposed a theoretical approach to temperature locality based on quantum estimation theory
Our method deals with the construction of the local quantum thermal susceptibility, which operationally highlights the degree at which the thermal equilibrium of the global system is perceived locally, avoiding any additional hypothesis on the local structure of the system
Summary
Thermodynamics relies on the possibility to describe systems composed of a large number of constituents in terms of few macroscopic variables. A lot of attention has been devoted to the search for novel methods of precision nanothermometry that could exploit the essence of quantum correlations[23,24,25,26,27,28] In this context, the possibility to correctly define the thermodynamical limit, and the existence of the temperature in the quantum regime, has been thoroughly investigated. In this regime, even for a tiny size of the probed subsystem, our functional is able to predict the behaviour of the heat capacity and in particular to reveal the presence of critical regions. This naturally suggests the interpretation of SA as a sort of mesoscopic version of the heat capacity, which replaces the latter in those regimes where extensivity breaks down
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