Thermodynamics of classifiers
Abstract
The rise of artificial intelligence has led to a growing demand for computational power. In this situation, energy-efficient computing methods are being actively investigated, which raises a fundamental question: what is the relationship between computational error and thermodynamic cost? Here, we derive the error-cost trade-off in the binary classifier by considering classification based on nonequilibrium thermodynamics. We derive trade-off relations showing that classification error cannot be lower than fundamental bounds set by thermodynamic quantities: entropy production, which measures irreversibility, and dynamical activity, which quantifies the activity of the system. Our results show that when entropy production or dynamical activity vanishes, the classification error reaches 1/2, equivalent to random guessing, whereas greater thermodynamic costs enable lower error. The results establish a quantitative trade-off in physical information processing, potentially leading to the development of energy-efficient computing devices.
Related
- From hyperplanes to hyperellipsoids: a pedagogical bridge from linear classifiers to single-qubit mixed-state classifiers
- Physical limits to stochastic classifiers
- A comparative study of variational quantum classifiers and classical machine learning for tW−tt̅ discrimination at the LHC
- Quantifying the Hadamard Resilience Effect and the Coherence Gap in NISQ-Era Classifiers
- Neural networks become centroid classifiers when trained on heavily corrupted inputs
BibTeX
@misc{hasegawa2026thermodynamics,
title = {{Thermodynamics of classifiers}},
author = {Yoshihiko Hasegawa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.24365},
eprint = {2605.24365},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.24365},
}
RIS
TY - UNPB
TI - Thermodynamics of classifiers
AU - Yoshihiko Hasegawa
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2605.24365
UR - https://arxiv.org/abs/2605.24365
AB - The rise of artificial intelligence has led to a growing demand for computational power. In this situation, energy-efficient computing methods are being actively investigated, which raises a fundamental question: what is the relationship between computational error and thermodynamic cost? Here, we derive the error-cost trade-off in the binary classifier by considering classification based on nonequilibrium thermodynamics. We derive trade-off relations showing that classification error cannot be lower than fundamental bounds set by thermodynamic quantities: entropy production, which measures irreversibility, and dynamical activity, which quantifies the activity of the system. Our results show that when entropy production or dynamical activity vanishes, the classification error reaches 1/2, equivalent to random guessing, whereas greater thermodynamic costs enable lower error. The results establish a quantitative trade-off in physical information processing, potentially leading to the development of energy-efficient computing devices.
ER -