Theoretical bound of the efficiency of learning

TL;DR

This paper introduces a thermodynamic framework that establishes fundamental bounds on the efficiency of learning processes, applicable to quantum systems and biological networks, revealing a trade-off between energy and information.

Contribution

It derives a new inequality surpassing Clausius's inequality to set the lower bound of entropy production and determines the maximum efficiency of learning.

Findings

Derived a stronger inequality than Clausius's for entropy production.

Established a universal upper limit for learning efficiency.

Applied the framework to quantum-dot systems and biological networks.

Abstract

A unified thermodynamic formalism describing the efficiency of learning is proposed. First, we derive an inequality, which is more strength than Clausius's inequality, revealing the lower bound of the entropy-production rate of a subsystem. Second, the inequality is transformed to determine the general upper limit for the efficiency of learning. In particular, we exemplify the bound of the efficiency in nonequilibrium quantum-dot systems and networks of living cells. The framework provides a fundamental trade-off relationship between energy and information inheriting in stochastic thermodynamic processes.