A Hyperbolic Free-Energy Framework for Neural Dynamics: Thermodynamic Principles Underlying Brain State Transitions and Cognitive Behaviors

Abstract

The brain is a dissipative, far-from-equilibrium system that continuously consumes energy to sustain structured neural activity while producing entropy. How system-level interactions among energy, entropy, structure, and physiological constraints give rise to cognition through distributed computation remains a central challenge in neuroscience. Existing free-energy frameworks have provided valuable conceptual insights, yet many remain largely metaphorical and lack explicit biological grounding, limiting the specificity and falsifiability of their predictions. Here, we propose a biologically grounded, thermodynamically inspired framework in which brain dynamics emerge from a continual balance between stability and flexibility, formalized as minimizing a Gibbs-free-energy-like function (ΔG = ΔH − TΔS). Stable neural configurations correspond to low-enthalpy, ordered states that support reliable function, whereas flexible configurations correspond to higher-entropy states that enable adaptive behavior. We further propose that neural population dynamics can be described as evolving on a hyperbolic statistical landscape shaped by metabolic, biophysical, anatomical, and bodily constraints. Neural activity samples this landscape, and experience gradually reshapes it over time. Metastable brain states occupy local free-energy minima, with transitions governed by Boltzmann-like probabilities. Learning sculpts the landscape via synaptic optimization and pruning, reducing entropy and stabilizing task-relevant dynamics. Importantly, this framework accounts for adaptive reallocation of neural resources under physiological stress, whereby higher-order cognitive functions may be transiently constrained to prioritize survival-essential processes, thereby predicting that cognitive function can remain rescuable in some cases despite structural damage. Together, this quantitative thermodynamic and geometric framework provides a unified foundation for understanding cognition as an emergent, system-level property of whole-brain dynamics.