Global optimization and monotonicity in entropy production of weak drivings
arXiv:2210.11975 · doi:10.1103/PhysRevE.107.024120
Abstract
Knowing if an optimal solution is local or global has always been a hard question to answer in more sophisticated situations of optimization problems. In this work, for finite-time and weak isothermal driving processes, we show the existence of a global optimal protocol for the entropy production. We prove that by showing its convexity as a functional in the derivative of the protocol. This property also proves its monotonicity in such a context, which leads to the satisfaction of the Second Law of Thermodynamics. In the end, we exemplify that the analytical technique of the Euler-Lagrange equation applied to overdamped Brownian motion delivers the global optimal protocol, by comparing it with the results of the global optimization technique of genetic programming.
arXiv comment6 pages, 2 figures
References in corpus (15)
- A nonequilibrium equality for free energy differences
- Entropy production along a stochastic trajectory and an integral fluctuation theorem
- Irreversible entropy production, from quantum to classical
- Optimal finite-time processes in stochastic thermodynamics
- Inertial self-propelled particles
- The Entropy Production of Ornstein-Uhlenbeck Active Particles: a path integral method for correlations
- Thermodynamic control -- an old paradigm with new applications
- Shortcuts to adiabaticity from linear response theory
- Minimal dissipation in processes far from equilibrium
- Degenerate optimal paths in thermally isolated systems
- Compatibility of linear-response theory with the Second Law of Thermodynamics and the emergence of negative entropy production rates
- Negative entropy production rates in Drude-Sommerfeld metals
- Performance of optimal linear-response processes in driven Brownian motion far from equilibrium
- Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems
- Fluctuation theorem for irreversible entropy production in electrical conduction