Toward a Physical Theory of Intelligence

TL;DR

This work advances a physics-grounded theory of intelligence by formulating intelligence as the rate at which irreversible information processing is converted into goal-directed work, χ = W_{ ext{goal}} / I_{ ext{irr}}$, with instantaneous and horizon variants. It builds a substrate-neutral framework (CCE) tying encodings to metastable basins protected by conserved quantities, and it leverages a GENERIC-like reversible–dissipative decomposition to separate structure-preserving dynamics from entropy-producing processes. The theory predicts that oscillatory and near-critical dynamics optimize the information-to-work tradeoff, and it develops a continuous-dynamical-circuit formalism in which Boolean logic emerges as a special case of attractor selection under CCE, enabling richer computational modes. It also addresses emergent intelligence, consciousness (as preserved information), epistemic limits, and safety, offering physically grounded guidelines for robust, symbiotic AI design and evaluation. Across experiments with reversible limits, substrate efficiency, reservoir near-criticality, and energy-constrained cellular automata, the results illustrate substantial reductions in irreversible information cost and highlight geometry-aligned computation as a path to efficient intelligence with clear safety implications.

Abstract

We present a physical theory of intelligence grounded in irreversible information processing in systems constrained by conservation laws. An intelligent system is modelled as a coupled agent-environment process whose evolution transforms information into goal-directed work. To connect information to physical state, we introduce the Conservation-Congruent Encoding (CCE) framework, in which encodings correspond to metastable basins of attraction whose separability is enforced by conservation laws. Within this framework, intelligence is defined as the amount of goal-directed work produced per nat of irreversibly processed information. From this definition we derive a hierarchy of physical constraints governing information intake, irreversible computation, and work extraction in open systems. The framework reveals how long-horizon efficiency requires the preservation of internal informational structure, giving rise to self-modelling, and it establishes that physically embodied intelligent systems possess intrinsic epistemic limits analogous to incompleteness phenomena. Applying the theory to biological systems, we analyse how oscillatory and near-critical dynamics optimise the trade-off between information preservation, dissipation, and useful work, placing the brain near an efficient operating regime predicted by the framework. At the architectural level, we develop a theory of continuous dynamical circuits in which classical Boolean logic emerges as a special case of attractor selection, while more general invariant geometries support computational modes beyond fixed-point logic. Finally, we propose a physically grounded perspective on artificial intelligence safety based on irreversible information flow and structural homeostasis. Together, these results provide a unified, substrate-neutral account of intelligence as a physical phenomenon.

Figures (9)

• Figure 1: Phase–space trajectories illustrating reversible versus dissipative internal dynamics. Left: A purely skew–symmetric flow generates a closed orbit with constant radius, preserving phase–space volume and producing zero generalized entropy. Right: Adding a symmetric, contractive component yields a dissipative spiral whose shrinking radius reflects irreversible loss of phase–space volume and positive entropy production. This contrast illustrates the reversible–dissipative decomposition central to the informational efficiency framework developed in this work.
• Figure 2: Three views of a coupled-oscillator dynamical circuit. (A) A one-dimensional phase oscillator with input, output, logical, and context ports. (B) Bidirectional coupling of two such oscillators. (C) The resulting joint state space on the torus $S^{1}\!\times S^{1}$, showing phase-locked and drifting regimes that yield discrete logical states under CCE-compliant encoding.
• Figure 3: Bistable memory implemented by mutually inhibiting, self-exciting activation nodes. The circuit admits two stable attractors $(x_A\text{ high},x_B\text{ low})$ and $(x_A\text{ low},x_B\text{ high})$ under CCE.
• Figure 4: Encoding path lengths in oscillator-based vs. digital frequency discrimination. (A) A forced oscillator collapses directly into one of two metastable attractors (locked vs. drifting); the encoding path length is $O(1)$. (B) A digital implementation must traverse a long chain of intermediate encodings (e.g. counters, comparators, registers), yielding $\Omega(1/\varepsilon)$ irreversible distinctions for resolution $\varepsilon$.
• Figure 5: (a) Total memory capacity $\mathrm{MC}(\lambda)$ remains high in the reversible and weakly dissipative regimes, decreasing only when $\lambda$ becomes large. (b) Irreversible-information rate $\dot I_{\mathrm{irr}}(\lambda)$, which increases linearly with the dissipation parameter. (c) Intelligence efficiency $\chi(\lambda)$ therefore decreases monotonically with increasing dissipation and is maximized in the reversible limit.

Theorems & Definitions (10)

• Proposition 6.1: State incompleteness
• proof : Proof sketch
• Proposition 6.2: Dynamical incompleteness
• Proposition 7.1: Minimal irreversible information among admissible metriplectic dynamics for fixed useful work
• proof : Proof sketch
• Corollary 7.1: Oscillatory Dynamics Approach the TUR Limit
• Corollary 7.2: Reversible Predictive Memory Reduces Irreversible Cost
• Proposition 7.2: Near-critical susceptibility enhances information efficiency
• proof : Proof sketch
• Proposition 9.1: Symbiosis Implies Emergent Intelligence