2017/05/22 by Erik Aurell · 23 citations
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Coupling (piping) #Entropy (arrow of time) #Harmonic oscillator #Limit (mathematics) #Quantum #Quantum many-body systems #Quantum thermodynamics #Thermal #Thermoelastic and Magnetoelastic Phenomena #Von Neumann entropy #Work (physics) #cond-mat.mes-hall #cond-mat.stat-mech
paper · pdf · doi:10.3390/e19110595
published in Entropy 19(11), 595 (Multidisciplinary Digital Publishing Institute)
arxiv created 2017/05/22 · openalex created_date 2017/06/05 · openalex publication_date 2017/11/07 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/05
This paper revisits the classical problem of representing a thermal bath interacting with a system as a large collection of harmonic oscillators initially in thermal equilibrium. As is well known, the system then obeys an equation, which in the bulk and in the suitable limit tends to the Kramers–Langevin equation of physical kinetics. I consider time-dependent system-bath coupling and show that this leads to an additional harmonic force acting on the system. When the coupling is switched on and switched off rapidly, the force has delta-function support at the initial and final time. I further show that the work and heat functionals as recently defined in stochastic thermodynamics at strong coupling contain additional terms depending on the time derivative of the system-bath coupling. I discuss these terms and show that while they can be very large if the system-bath coupling changes quickly, they only give a finite contribution to the work that enters in Jarzynski’s equality. I also discuss that these corrections to standard work and heat functionals provide an explanation for non-standard terms in the change of the von Neumann entropy of a quantum bath interacting with a quantum system found in an earlier contribution (Aurell and Eichhorn, 2015).