A thermoinformational formulation for the description of neuropsychological systems

Abstract

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.

Figures (6)

• Figure 1: (A) Framework Flowchart. (B)$(S,U)$ state-space schematic with example displacements; $\Delta Q>0$ = positive informational heat (reconfiguration). Illustrative regime labels (lower $T,F_H$ vs. higher $T,Q$) aiding in general interpretability of framework's results.
• Figure 2: Thermoinformational variables during toy switch versus no-switch trials. (A) Child heat ($Q$) per pair, (B) child temperature ($T$), (C) child Helmholtz free energy ($F$), and (D) adult internal energy ($U$) all show significant differences between conditions ($p<0.05$). Heat increases during switch trials, marking stronger informational reconfiguration when the environment changes. Temperature likewise increases, indicating a robust high-repertoire regime supporting adaptation. Both free energy and adult internal energy decrease, consistent with more efficient and stable configurations after reorganization. Together, these results highlight a coherent thermodynamic pattern: high $Q$ and $T$ accompany reconfiguration, whereas low $F$ and $U$ signal stabilization and efficiency.
• Figure 3: Thermoinformational variables during correct versus incorrect responses. (A) Child Helmholtz free energy ($F$) and (B) child temperature ($T$) show significant differences between correct and incorrect trials ($p<0.05$). Correct choices are associated with slightly higher free energy and lower temperature, suggesting that successful retrieval involves transient increases in informational work capacity followed by efficient stabilization. These complementary patterns reinforce the interpretation that thermoinformational variables differentiate phases of reconfiguration and stabilization within adaptive neural behavior.
• Figure 4: In this figure the mean values and standard deviations of the different thermoinformational variables are presented for the interaction phase. In subfigure A the entropy is displayed. The No Opto condition has higher entropy values with strong statistical significance. In subfigure B the internal energy is displayed, with the No Opto condition having higher values with a Welch's t-test p-value $\le10^{-6}$. Subfigure C shows the temperature, with the No Opto condition having higher values but not statistically significant with a Welch's t-test p-value of 0.2053. Lastly in subfigure D the Cv shows higher values for the Opto condition instead with a Welch's t-test p-value of 0.0035.
• Figure 5: In this figure the mean values and standard deviations of the different thermoinformational variables are presented for the foraging phase. In subfigure A the entropy is displayed. The No Opto condition has higher entropy values with a Welch's t-test p-value 0.0201. In subfigure B the internal energy is displayed, with the No Opto condition having higher values with a Welch's t-test p-value 0.0181. Subfigure C shows the temperature, with the No Opto condition having higher values with a Welch's t-test p-value of 0.0433. Lastly in subfigure D while the Cv shows higher values for the Opto condition the difference is not statistically significant with a Welch's t-test p-value of 0.164