Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Hasegawa, Yoshihiko
Institution: The University of Tokyo
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162435476