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.

中文翻译：

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学习效率的理论界限

提出了一种描述学习效率的统一热力学形式。首先，我们推导出一个比克劳修斯不等式更有力的不等式，它揭示了子系统熵产率的下界。其次，转化不等式以确定学习效率的一般上限。特别是，我们举例说明了非平衡量子点系统和活细胞网络的效率界限。该框架提供了随机热力学过程中能量和信息继承之间的基本权衡关系。