Minimax entropy production for arbitrary processes
Abstract
For any physical process, varying the initial distribution over its states will change the resulting expected entropy production (EP). An initial distribution that minimizes the EP of a particular process is called the prior of that process. Varying the microphysical details of the process will change its prior. We consider the following question: if an engineer wants to design a system to implement a given map, what prior should they design into the system to minimize the EP for the worst-case actual distribution? We refer to the resulting optimal worst-case value as the minimax EP, and investigate how it depends only on the dynamics of the process. We derive the closed-form solution to this minimax problem when the map is deterministic. We also show that for stochastic maps, a worst-case actual distribution can always be chosen to be a point mass on a single state, and that the associated minimax prior resembles a Boltzmann-Gibbs equation and can be found by a globally convergent numerical algorithm. We further show that the minimax EP is the maximum uncertainty about the input that remains after observing the output. Finally, we extend the analysis to the continuous-time regime, showing that the minimax instantaneous EP diverges, while the corresponding finite-time minimax EP has a universal short-time scaling set by the largest escape rate of the dynamics.
Related
- Covering Surfaces, Conical-Defect Continuation, and Multi-Entropy at Arbitrary Genus
- Explicit Boundary-Entropy Deficits in the XX Spin Chain with arbitrary boundary fields
- Obstruction to local entropy laws on arbitrary black-hole cuts in five-dimensional Einstein--Gauss--Bonnet gravity
- Stochastic synthesis and degradation of arbitrary diffusive processes
- Haar-Bayesian Pure-State Prediction under Relative-Entropy Loss: Arbitrary-Effect Reduction and Global Optimality
BibTeX
@misc{yousef2026minimax,
title = {{Minimax entropy production for arbitrary processes}},
author = {Mahran Yousef and Ben Ansbacher and David H. Wolpert},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03478},
eprint = {2610.03478},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03478},
}
RIS
TY - UNPB
TI - Minimax entropy production for arbitrary processes
AU - Mahran Yousef
AU - Ben Ansbacher
AU - David H. Wolpert
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.03478
UR - https://arxiv.org/abs/2610.03478
AB - For any physical process, varying the initial distribution over its states will change the resulting expected entropy production (EP). An initial distribution that minimizes the EP of a particular process is called the prior of that process. Varying the microphysical details of the process will change its prior. We consider the following question: if an engineer wants to design a system to implement a given map, what prior should they design into the system to minimize the EP for the worst-case actual distribution? We refer to the resulting optimal worst-case value as the minimax EP, and investigate how it depends only on the dynamics of the process. We derive the closed-form solution to this minimax problem when the map is deterministic. We also show that for stochastic maps, a worst-case actual distribution can always be chosen to be a point mass on a single state, and that the associated minimax prior resembles a Boltzmann-Gibbs equation and can be found by a globally convergent numerical algorithm. We further show that the minimax EP is the maximum uncertainty about the input that remains after observing the output. Finally, we extend the analysis to the continuous-time regime, showing that the minimax instantaneous EP diverges, while the corresponding finite-time minimax EP has a universal short-time scaling set by the largest escape rate of the dynamics.
ER -