Complex systems produce high-dimensional signals that lack macroscopic variables analogous to entropy, temperature, or free energy. This work introduces a thermoinformational formulation that derives entropy, internal energy, temperature, and Helmholtz free energy directly from empirical microstate distributions of arbitrary datasets. The approach provides a data-driven description of how a system reorganizes, exchanges information, and moves between stable and unstable states. Applied to dual-EEG recordings from mother-infant dyads performing the A-not-B task, the formulation captures increases in informational heat during switches and errors, and reveals that correct choices arise from more stable, low-temperature states. In an independent optogenetic dam-pup experiment, the same variables separate stimulation conditions and trace coherent trajectories in thermodynamic state space. Across both human and rodent systems, this thermoinformational formulation yields compact and physically interpretable macroscopic variables that generalize across species, modalities, and experimental paradigms.

翻译：复杂系统产生的高维信号缺乏类似于熵、温度或自由能等宏观变量。本研究提出一种热信息学理论框架，能够直接从任意数据集的微观状态经验分布推导出熵、内能、温度及亥姆霍兹自由能。该方法通过数据驱动的方式描述系统如何重组、交换信息以及在稳定态与非稳定态之间转换。将本框架应用于执行A-not-B任务的母婴双人脑电记录时，该理论成功捕捉到状态切换与错误发生时信息热量的增加，并揭示正确选择产生于更稳定、低温度的状态。在独立的光遗传学母鼠-幼鼠实验中，相同变量能够区分不同刺激条件，并在热力学状态空间中描绘出连贯的轨迹。在人类与啮齿类动物系统中，该热信息学理论框架均能产生紧凑且具物理解释性的宏观变量，其适用性跨越物种、模态及实验范式。