Computing the optimal protocol for finite-time processes in stochastic thermodynamics

Computing the optimal protocol for finite-time processes in stochastic thermodynamics.

Asking for the optimal protocol of an external control parameter that minimizes the mean work required to drive a nanoscale system from one equilibrium state to another in finite time, Schmiedl and Seifert [T. Schmiedl and U. Seifert, Phys. Rev. Lett. 98, 108301 (2007)] found the Euler-Lagrange equation to be a nonlocal integrodifferential equation of correlation functions. For two linear examp...

Optimal processes in Stochastic Thermodynamics

Optimal Stochastic Control in Continuous Time with Wiener Processes: General Results and Applications to Optimal Wildlife Management

We present a stochastic optimal control approach to wildlife management. The objective value is the present value of hunting and meat, reduced by the present value of the costs of plant damages and traffic accidents caused by the wildlife population. First, general optimal control functions and value functions are derived. Then, numerically specified optimal control functions and value func...

Time reversibility and nonequilibrium thermodynamics of second-order stochastic processes.

Nonequilibrium thermodynamics of a general second-order stochastic system is investigated. We prove that at steady state, under inversion of velocities, the condition of time reversibility over the phase space is equivalent to the antisymmetry of spatial flux and the symmetry of velocity flux. Then we show that the condition of time reversibility alone cannot always guarantee the Maxwell-Boltzm...

Finite-time Thermodynamics Tools to Analyze Dissipative Processes

“Staging free energy” is a term introduced to describe the necessary investment of free energy into a thermodynamic system to allow certain near equilibrium processes to proceed in a desired direction and in finite time (Chapter 4). Such processes may seem—if viewed detached from their surroundings—to be truly reversible. However, if one views them together with the changes occurring in their e...