A thermoinformational formulation for the description of neuropsychological systems

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.

💡 Research Summary

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The paper introduces a novel “thermoinformational” framework that extracts classic thermodynamic quantities—entropy, internal energy, temperature, specific heat, and Helmholtz free energy—directly from empirical microstate distributions of any high‑dimensional dataset. The authors first formalize a microstate as the smallest measurable vector of a system (e.g., a set of EEG features at a given time point) and assemble all observations into a multidimensional tensor A = X{t,n,i}. From this tensor they estimate a continuous probability density p(E) using kernel density estimation (or other suitable methods) and compute Shannon entropy S = −∫p(E)ln p(E)dE and internal energy U = ∫|E|p(E)dE, where |E| is the L2 norm for vector‑valued microstates.

Temperature is defined via the thermodynamic relation 1/T = ∂S/∂U. Because S(U) is only known numerically, the authors perturb the KDE bandwidth λ by a small factor (1 + Δλ) to generate a slightly altered density pλ+Δλ, recompute S and U, and approximate the derivative dS/dU as (Sλ+Δλ − Sλ)/(Uλ+Δλ − Uλ). The reciprocal yields T. Specific heat at constant volume Cv = T·dS/dT is obtained analogously, and Helmholtz free energy follows as FH = U − TS. This pipeline produces a self‑consistent set of macroscopic variables that are grounded in the data rather than imposed a priori.

Two very different experimental contexts are used to validate the approach. In the first, dual‑EEG recordings from mother‑infant dyads performing the classic A‑not‑B task are analyzed. Each trial is converted into a microstate, and the thermoinformational variables are tracked across time. The authors find that “informational heat” ΔQ (the product T·ΔS) spikes during rule switches and error trials, reflecting a surge of configurational reorganization. Correct choices, by contrast, are associated with low temperature, low free‑energy states, suggesting that successful decision‑making corresponds to a thermodynamically stable basin. This provides a quantitative, physics‑based refinement of the “entropic brain” hypothesis, showing that high entropy can coexist with low temperature when the system is efficiently organized.

The second validation involves optogenetically driven synchrony in the prefrontal cortex of rodent dams and pups. Different light‑stimulation protocols (e.g., low‑frequency vs. high‑frequency pulses) generate distinct trajectories in the (S,U) state space. Temperature, entropy, and free energy separate cleanly between conditions, and the direction of ΔQ indicates whether the network is being “heated” (entering a high‑repertoire, exploratory regime) or “cooled” (settling into a coordinated, low‑entropy state). These results demonstrate that the framework can capture rapid, stimulus‑induced phase‑transition‑like dynamics in vivo.

Conceptually, the work bridges the gap between the free‑energy principle (FEP), which treats free energy as an information‑theoretic bound on model evidence, and classical thermodynamics, where Helmholtz free energy governs physical equilibrium. By estimating a genuine thermodynamic temperature from data, the authors show that neural systems can simultaneously increase entropy and temperature (high‑repertoire exploration) or lower both (stable cognition), depending on task demands. The inclusion of specific heat further allows detection of critical points where small energy inputs produce large entropy changes, reminiscent of phase transitions in statistical physics.

The authors acknowledge several limitations. The KDE bandwidth strongly influences the estimated density, and thus all derived quantities; systematic bandwidth selection or cross‑validation is essential. The framework assumes a quasi‑steady‑state distribution for each analysis window, which may not hold during rapid transients. Moreover, the physical interpretation of temperature and heat in a purely informational system requires caution; they are analogues rather than literal thermodynamic variables. Nevertheless, the ability to translate arbitrary high‑dimensional neuro‑behavioral data into a compact set of physically interpretable macroscopic variables is a powerful advance.

In summary, this study provides a general, data‑driven thermodynamic formalism for neuropsychological systems. It demonstrates that entropy, internal energy, temperature, and free energy can be meaningfully derived from EEG and optogenetic recordings, that these variables capture meaningful cognitive events (errors, switches, correct decisions), and that they generalize across species and experimental modalities. The thermoinformational approach opens new avenues for quantifying brain state dynamics, detecting reconfiguration events, and unifying diverse complex‑system phenomena under a common physical language.