Optimal time-entropy bounds and speed limits for Brownian thermal shortcuts

TL;DR

This paper develops optimal control protocols for rapid thermal state transfer in microspheres, establishing fundamental speed limits and entropic bounds that enhance the design of efficient mesoscale thermodynamic cycles.

Contribution

It introduces a framework for optimizing temperature protocols to minimize entropy production or maximize transfer speed, revealing fundamental bounds on thermalization processes.

Findings

Derived time-entropy bounds for thermal shortcuts.

Designed optimal temperature protocols minimizing entropy.

Expanded possibilities for finite-time Brownian thermalization.

Abstract

By controlling in real-time the variance of the radiation pressure exerted on an optically trapped microsphere, we engineer temperature protocols that shortcut thermal relaxation when transferring the microsphere from one thermal equilibrium state to an other. We identify the entropic footprint of such accelerated transfers and derive optimal temperature protocols that either minimize the production of entropy for a given transfer duration or accelerate as much as possible the transfer for a given entropic cost. Optimizing the trade-off yields time-entropy bounds that put speed limits on thermalization schemes. We further show how optimization expands the possibilities for accelerating Brownian thermalization down to its fundamental limits. Our approach paves the way for the design of optimized, finite-time thermodynamic cycles at the mesoscale. It also offers a platform for investigating fundamental connections between information geometry and finite-time processes.