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arXiv · 2110.03758

Taming the time evolution in overdamped systems: shortcuts elaborated from fast-forward and time-reversed protocols

Carlos A. Plata·Antonio Prados·Emmanuel Trizac·David Guéry-Odelin
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Abstract

Using a reverse-engineering approach on the time-distorted solution in a reference potential, we work out the external driving potential to be applied to a Brownian system in order to slow or accelerate the dynamics, or even to invert the arrow of time. By welding a direct and time-reversed evolution towards a well chosen common intermediate state, we derive analytically a smooth protocol to connect two \emph{arbitrary} states in an arbitrarily short amount of time. Not only does the reverse-engineering approach proposed in this Letter contain the current -- rather limited -- catalogue of explicit protocols but it also provides a systematic strategy to build the connection between arbitrary states with a physically admissible driving. Optimization and further generalizations are also discussed.

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Carlos A. Plata, Antonio Prados, Emmanuel Trizac, David Guéry-Odelin. 2021-10-07. Taming the time evolution in overdamped systems: shortcuts elaborated from fast-forward and time-reversed protocols. https://doi.org/10.1103/physrevlett.127.190605

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