Near-optimal protocols in complex nonequilibrium transformations

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 113; no. 37
• Main Authors: Gingrich, Todd R., Rotskoff, Grant M., Crooks, Gavin E., Geissler, Phillip L.
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences, Washington, DC (United States) 29.08.2016
• Subjects: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; entropic sampling methods; irreversible thermodynamics; Ising model; MATHEMATICS AND COMPUTING; Metropolis algorithm; nonequilibrium
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.1606273113

The development of sophisticated experimental means to control nanoscale systems has motivated efforts to design driving protocols that minimize the energy dissipated to the environment. Computational models are a crucial tool in this practical challenge. In this paper, we describe a general method for sampling an ensemble of finite-time, nonequilibrium protocols biased toward a low average dissipation. In addition, we show that this scheme can be carried out very efficiently in several limiting cases. As an application, we sample the ensemble of low-dissipation protocols that invert the magnetization of a 2D Ising model and explore how the diversity of the protocols varies in response to constraints on the average dissipation. In this example, we find that there is a large set of protocols with average dissipation close to the optimal value, which we argue is a general phenomenon.