Optimal control in nonisothermal stochastic systems: temperature-driven and potential-driven protocols

Cin-Hua Pan^1*, Pik-Yin Lai¹

¹Department of Physics, National Central University, Taoyuan, Taiwan
²Department of Physics, National Central University, Taoyuan, Taiwan

* Presenter:Cin-Hua Pan, email:andy0929539033@gmail.com

We investigate optimal control in nonisothermal stochastic systems, aiming to minimize total entropy production during finite-time transitions between nonequilibrium distributions. The potential or temperature fields are allowed to vary with time. By designing specific functional forms for these fields, the dynamics can be mapped onto an equivalent Ornstein–Uhlenbeck process, yielding a reduced description in terms of a few control parameters. The optimal protocol is obtained through the Pontryagin minimum principle (PMP), leading to a pair of coupled ordinary differential equations analogous to those in finite-time thermodynamic optimization. Owing to the presence of an anomalous entropy term intrinsic to nonuniform temperature systems, the optimal protocol may exhibit oscillatory behavior, particularly during long compression processes. Consequently, a minimal protocol duration exists that minimizes total entropy production. This framework offers new insights into information erasure processes driven by time-dependent, spatially nonuniform temperature fields.

Keywords: Optimal protocol, Pontryagin's principle, Non-equilibrium system, Landauer principle, Information erasure