2019/07/12 by Philippe Faist, Takahiro Sagawa, Kohtaro Kato +2
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Ergodic theory #Gibbs state #Hamiltonian (control theory) #Mathematics #Non-equilibrium thermodynamics #Observable #Physics #Pure mathematics #Quantum #Quantum many-body systems #Quantum mechanics #Quantum thermodynamics #Second law of thermodynamics #Statistical Mechanics and Entropy #Statistical physics #Thermal equilibrium #Thermodynamic equilibrium #Thermodynamics #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physrevlett.123.250601
published as Phys. Rev. Lett. 123, 250601 (2019) · 5 pages + references, 2 figures. Short companion paper to our technical paper published today on the arXiv
arxiv created 2019/07/12 · openalex publication_date 2019/12/17 · arxiv updated 2019/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The resource theory of thermal operations, an established model for small-scale thermodynamics, provides an extension of equilibrium thermodynamics to nonequilibrium situations. On a lattice of any dimension with any translation-invariant local Hamiltonian, we identify a large set of translation-invariant states that can be reversibly converted to and from the thermal state with thermal operations and a small amount of coherence. These are the spatially ergodic states, i.e., states that have sharp statistics for any translation-invariant observable, and mixtures of such states with the same thermodynamic potential. As an intermediate result, we show for a general state that if the gap between the min- and the max-relative entropies to the thermal state is small, then the state can be approximately reversibly converted to and from the thermal state with thermal operations and a small source of coherence. Our proof provides a quantum version of the Shannon-McMillan-Breiman theorem for the relative entropy and a quantum Stein's lemma for ergodic states and local Gibbs states. Our results provide a strong link between the abstract resource theory of thermodynamics and more realistic physical systems as we achieve a robust and operational characterization of the emergence of a thermodynamic potential in translation-invariant lattice systems.