Related Experiment Video
Updated: Aug 6, 2025

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
Published on: March 30, 2017
Global optimization and monotonicity in entropy production of weak drivings
1Departamento de Ciências Exatas e Tecnológicas, Universidade Federal do Amapá, 68903-419, Macapá, Amapá, Brazil.
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 paper, for finite-time and weak isothermal driving processes, we show the existence of a global optimal protocol for the entropy production. We prove this 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.
Related Concept Videos
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Entropy and the Second Law of Thermodynamics
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
Entropy
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
Second Law of Thermodynamics
The Second Law of Thermodynamics
Statements of the Second Law of Thermodynamics

