2016/11/30 by Robert S. Whitney · 50 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #First law of thermodynamics #Fluctuation theorem #Homogeneous space #Laws of thermodynamics #Mathematics #Non-equilibrium thermodynamics #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Quantum mechanics #Quantum thermodynamics #Quantum tunnelling #Second law of thermodynamics #Statistical physics #Work (physics) #cond-mat.mes-hall #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physrevb.98.085415
published in Physical review. B./Physical review. B 98(8) (American Physical Society) · This version corrects an error in Section VIII D of the version published in Phys. Rev. B (an error in the condition for the validity of the Crooks equaton)
openalex publication_date 2018/08/07 · arxiv created 2021/03/14 · arxiv updated 2021/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This work brings together thermodynamics and nonequilibrium quantum theory, by showing that a real-time diagrammatic technique on the Keldysh contour is an equivalent of stochastic thermodynamics for non-Markovian quantum machines (heat engines, refrigerators, etc.). Symmetries are found between quantum trajectories and their time reverses on the Keldysh contour, for any interacting quantum system coupled to ideal reservoirs of electrons, phonons, or photons. These lead to quantum fluctuation theorems the same as the well-known classical ones (Jarzynski and Crooks equalities, integral fluctuation theorem, etc.), whether the system's dynamics are Markovian or not. Some of these are also shown to hold for nonfactorizable initial states. The sequential tunneling approximation and the cotunneling approximation are both shown to respect the symmetries that ensure the fluctuation theorems. For all initial states, energy conservation ensures that the first law of thermodynamics holds on average, while the above symmetries ensure that the second law of thermodynamics holds on average, even if fluctuations violate it.