Coarse-Grained Quantum Thermodynamics: Observation-Dependent Quantities, Observation-Independent Laws

TL;DR

This paper investigates how limited measurement precision in quantum thermodynamics affects the definition and interpretation of thermodynamic quantities, revealing that some properties depend on observation, yet fundamental relations remain consistent.

Contribution

It introduces the concept of observation-dependent thermodynamic quantities and demonstrates their impact on process irreversibility and work, while preserving key thermodynamic relations.

Findings

Coarse-grained quantities can alter conclusions about irreversibility and work.

Fundamental thermodynamic relations hold despite observation-dependent definitions.

Observation influences the evaluation of thermodynamic processes in quantum systems.

Abstract

In both classical and quantum thermodynamics, physical quantities are typically assigned objective values defined independently of our observations. We then refer to the 'work performed by a gas', or the 'entropy of the gas', regardless of how they are evaluated. Here, we question this conception in the context of quantum thermodynamics, estimating how the definition of pivotal thermodynamic quantities is affected by experimental instruments of limited precision. We find that the coarse-grained thermodynamic quantities frequently lead to different conclusions from those drawn in fine-grained scenarios. For instance, the irreversibility of a process, or its work payoff, can significantly vary with the instrument precision. We show nonetheless that coarse-grained thermodynamic quantities satisfy the same relations (i.e., the second law inequality, the relation between dissipation and distinguishability of a process from its time-reverse, and the quantum work fluctuation theorems) as their fine-grained counterparts. These results highlight the observation-independence of relations linking thermodynamic quantities which are themselves observation-dependent.