2018/11/30 by Camilo Moreno, Juan-Diego Urbina, Juan Diego Urbina
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Brownian motion #Canonical ensemble #Coupling (piping) #Equivalence (formal languages) #Generalization #Ground state #Markov process #Mathematical analysis #Mathematical physics #Mathematics #Microcanonical ensemble #Monotonic function #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum many-body systems #Quantum mechanics #Quantum statistical mechanics #Saddle point #Statistical ensemble #Statistical physics #Statistics #Thermodynamic limit #quant-ph
paper · pdf · doi:10.1103/physreve.99.062135
published as Phys. Rev. E 99, 062135 (2019) · Extended version with additional clarifying information
openalex publication_date 2019/06/27 · arxiv created 2019/06/28 · arxiv updated 2019/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the emergence of temperature T in the system-plus-reservoir paradigm starting from the fundamental microcanonical scenario at total fixed energy E where, contrary to the canonical approach, T=T(E) is not a control parameter but a derived auxiliary concept. As shown by Schwinger for the regime of weak coupling γ between subsystems, T(E) emerges from the saddle-point analysis leading to the ensemble equivalence up to corrections O(1/sqrt[N]) in the number of particles N that defines the thermodynamic limit. By extending these ideas for finite γ, while keeping N→∞, we provide a consistent generalization of temperature T(E,γ) in strongly coupled systems, and we illustrate its main features for the specific model of quantum Brownian motion where it leads to consistent microcanonical thermodynamics. Interestingly, while this T(E,γ) is a monotonically increasing function of the total energy E, its dependence with γ is a purely quantum effect notably visible near the ground-state energy and for large energies differs for Markovian and non-Markovian regimes.