Learning systems acquire structured internal representations from data, yet classical information-theoretic results state that deterministic transformations do not increase information. This raises a fundamental question: how can learning produce abstraction and insight without violating information-theoretic limits? We argue that learning is inherently an irreversible process when performed over finite time, and that the realization of epistemic structure necessarily incurs entropy production. To formalize this perspective, we model learning as a transport process in the space of probability distributions over model configurations and introduce an epistemic free-energy framework. Within this framework, we define the free-energy drop as a bookkeeping quantity that records the total reduction of epistemic free energy along a learning trajectory. This reduction decomposes into a reversible component associated with potential improvement and an irreversible component corresponding to entropy production. We then derive the Epistemic Speed Limit (ESL), a finite-time inequality that lower-bounds the minimal entropy production required by any learning process to realize a given distributional transformation. This bound depends only on the Wasserstein distance between initial and final ensemble distributions and is independent of the specific learning algorithm.

翻译：学习系统从数据中获取结构化的内部表征，然而经典信息论结果表明确定性变换不会增加信息。这引发了一个根本性问题：学习如何在遵循信息论极限的前提下产生抽象与洞见？我们认为，当学习在有限时间内进行时，其本质上是一个不可逆过程，并且认知结构的实现必然伴随着熵的产生。为形式化这一观点，我们将学习建模为模型配置概率分布空间中的输运过程，并引入认知自由能框架。在此框架内，我们将自由能下降定义为一个簿记量，用于记录学习轨迹上认知自由能的总减少量。该减少量可分解为与潜在改进相关的可逆分量和对应熵产生的不可逆分量。随后，我们推导出认知速度极限——一个有限时间不等式，该不等式为任何学习过程实现给定分布变换所需的最小熵产生量设定了下界。该下界仅取决于初始与最终系综分布之间的Wasserstein距离，且与具体学习算法无关。