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  • Open Access

Optimal computation from fluctuation responses

Jinghao Lyu*, Kyle J. Ray†, and James P. Crutchfield‡

  • *Contact author: jolyu@ucdavis.edu
  • †Contact author: kjray@ucdavis.edu
  • ‡Contact author: chaos@ucdavis.edu
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Phys. Rev. Research 8, 023253 – Published 8 June, 2026

DOI: https://doi.org/10.1103/8xjg-rbdm

Abstract

The energy cost of computation has emerged as a central challenge at the intersection of physics and computer science. Recent advances in statistical physics—particularly in stochastic thermodynamics—enable precise characterizations of work, heat, and entropy production in information-processing systems driven far from equilibrium by time-dependent control protocols. A key open question is then how to design protocols that minimize thermodynamic cost while ensuring correct outcomes. To this end, we develop a unified framework to identify optimal protocols using fluctuation-response relations (FRRs) and machine learning. Unlike previous approaches that optimize either distributions or protocols separately, our method unifies both using FRR-derived gradients. Moreover, our method is based primarily on iteratively learning from sampled noisy trajectories, which is generally much easier than solving for the optimal protocol directly from a set of governing equations. We apply the framework to canonical examples—bit erasure in a double-well potential and translating harmonic traps—demonstrating how to construct loss functions that trade-off energy cost against task error. The framework extends trivially to underdamped systems, and we show this by optimizing a bit flip in an underdamped system. In all computations we test, the framework achieves the theoretically optimal protocol or achieves work costs comparable to relevant finite-time bounds. In short, the results provide principled strategies for designing thermodynamically efficient protocols in physical information-processing systems. Applications range from quantum gates robust under noise to energy-efficient control of chemical and synthetic biological networks.

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Phys. Rev. Research 8, 023253– Published 8 June, 2026
  • Received 13 October 2025
  • Accepted 10 May 2026
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