Computational Mass of Living Matter: A Free‑Energy and Partition‑Theoretic Model of Consciousness

MathAI 2026 Conference Submission109 Authors

Keywords: free energy principle (FEP), active inference, Hardy–Ramanujan; Rademacher series, computational consciousness, AGI

Abstract:

We introduce a dimensionless construct—the computational mass of living matter—that links combinatorial internal complexity with adaptive inference under the free energy principle (FEP). The framework combines: (i) an extended mass–energy–information balance for living systems (motivated by a prior “living mass” decomposition), (ii) Markov-blanket and variational-free-energy formulations of self-organization and active inference, and (iii) Hardy–Ramanujan asymptotics together with Rademacher’s exact series for the integer partition function p(n). The discrete index n∈N is defined as a dimensionless complexity parameter derived from an energy (or information) scale, so that p(n) provides a mathematically controlled proxy for the growth of admissible internal configurations. We define
$M_comp (n)=Ψ p(n) exp (-F_eff (n))$,
where F_eff (n) is an effective (time-averaged, normalized) variational free energy and Ψ is a normalization constant. The partition term measures structural capacity; the exponential term penalizes poorly adapted, high-surprisal regimes as formalized by FEP. Using the asymptotics of log⁡p(n), we characterize monotonicity regions and critical regimes where marginal combinatorial gains are outweighed by marginal free-energy costs, yielding a phase-transition–like criterion for an operational notion of computational consciousness (efficient self-modeling under active inference). We also give rigorous upper/lower bounds on M_comp (n) and show how the definition specializes to variational generative AI models.

Submission Number: 109