# Optimal Computation from Fluctuation Responses

arXiv: https://arxiv.org/abs/2510.03900 · HTML: https://mlsanity.com/paper/2510.03900/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 106 references that are in the map.
- First posted on arXiv 4 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Learning entropy production via neural networks](https://mlsanity.com/paper/2003.04166/) (2020)
- [Training thermodynamic computers by gradient descent](https://mlsanity.com/paper/2509.15324/) (2025)
- [Demon in the machine: learning to extract work and absorb entropy from fluctuating nanosystems](https://mlsanity.com/paper/2211.10853/) (2022)
- [How to train your demon to do fast information erasure without heat production](https://mlsanity.com/paper/2305.10607/) (2023)
- [Wasserstein speed limits for Langevin systems](https://mlsanity.com/paper/2312.07788/) (2023)
- [Optimal Control of Underdamped Systems: An Analytic Approach](https://mlsanity.com/paper/2403.00679/) (2024)
- [Minimal work protocols for inertial particles in non-harmonic traps](https://mlsanity.com/paper/2407.15678/) (2024)

## Abstract (arXiv)

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 ensur- ing correct outcomes. To this end, we develop a unified framework to identify optimal protocols using fluctuation response relations (FRR) 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.