Optimal finite-time processes in weakly driven overdamped Brownian motion

Author(s)

Naze, Pierre ; Deffner, Sebastian ; Bonanca, Marcus V. S.

• Document type: Journal article
• Source: JOURNAL OF PHYSICS COMMUNICATIONS; v. 6, n. 8, p. 15-pg., 2022-08-01.

Abstract

The complete physical understanding of the optimization of the thermodynamic work still is an important open problem in stochastic thermodynamics. We address this issue using the Hamiltonian approach of linear response theory in finite time and weak processes. We derive the Euler-Lagrange equation associated and discuss its main features, illustrating them using the paradigmatic example of driven Brownian motion in overdamped regime. We show that the optimal protocols obtained either coincide, in the appropriate limit, with the exact solutions by stochastic thermodynamics or can be even identical to them, presenting the well-known jumps. However, our approach reveals that jumps at the extremities of the process are a good optimization strategy in the regime of fast but weak processes for any driven system. Additionally, we show that fast-but-weak optimal protocols are time-reversal symmetric, a property that has until now remained hidden in the exact solutions far from equilibrium. (AU)

• FAPESP's process: 18/06365-4 - Optimization of thermodynamical work in far from equilibrium systems
• Grantee: Pierre Marie Antoine Leite Nazé
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 20/02170-4 - Optimal thermodynamic processes in out-of-equilibrium systems
• Grantee: Marcus Vinicius Segantini Bonança
• Support Opportunities: Regular Research Grants
• FAPESP's process: 18/21285-7 - Optimization of thermodynamic work with machine learning control
• Grantee: Pierre Marie Antoine Leite Nazé
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate