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This research establishes a fundamental thermodynamic lower bound for the error rates of binary classifiers, linking computational accuracy directly to entropy production and dynamical activity. By deriving these trade-off relations within nonequilibrium thermodynamics, the study provides a theoretical framework for designing energy-efficient AI hardware that operates near physical limits. This work bridges statistical mechanics and machine learning, offering critical insights for the future of low-power information processing architectures.
Thermodynamics of classifiers
arXiv:2605.24365v3 Announce Type: replace-cross 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.
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.
Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
arXiv:2605.24365 [cond-mat.stat-mech]
(or arXiv:2605.24365v3 [cond-mat.stat-mech] for this version)
https://doi.org/10.48550/arXiv.2605.24365 Focus to learn more arXiv-issued DOI via DataCite
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