Cognitive Thermodynamics for Mnemoverse 2.0

Thermodynamic Principles in Cognitive Systems

This document presents a speculative framework applying thermodynamic laws to cognitive processes.
• For experimental validation protocols see Experimental Protocol.

Abstract

Modern research suggests that cognition can be described by physical principles: brains are far-from-equilibrium systems with hierarchical organization, arrows of time, and thermodynamic constraints. In analogy to physics, we hypothesize cognitive thermodynamics: fundamental laws governing how information and energy flow in mental processes. For example, Kringelbach & Deco (2024) propose a "Thermodynamics of Mind" framework to quantify the brain's hierarchical orchestration, finding that tasks like movie-watching produce a "flatter" hierarchy (i.e. more uniform information flow) than rest. Likewise, Deco et al. (2023) use a deep learning classifier to reveal the "arrow of time" in brain signals – a measure of non-reversibility and nonequilibrium – showing that the default-mode network orchestrates directed information flow across tasks. These studies highlight that cognitive states have entropy and flow patterns much like physical systems, motivating a theory of cognitive physics.

A useful mental model is to treat memory and cognition as a geometric field over a structured space. MnemoVerse defines a cognitive space , where is a hyperbolic cognitive manifold, embeds stimuli (semantics) into this space, is an activation (attention) field over , and evolves states in time. In this view, memories and concepts are continuous points or regions in , and attention "curves" the metric to make relevant memories closer (analogous to mass curving spacetime). The rigorous MnemoVerse axioms even ensure that memory diffuses and decays smoothly over time (modeling forgetting without catastrophic loss) while total "information energy" decays at a controlled rate.

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1. Thermodynamics in Cognition

Biological cognition obeys thermodynamic constraints. The brain must process information efficiently under energy limits, implying analogues of energy conservation and entropy. For example, Deli et al. (2021) analyze cognition as Carnot cycles: positive emotional states correspond to a reversed Carnot cycle and negative states to a forward Carnot cycle, yielding different entropy and energy aftereffects. Likewise, Friston's Free Energy Principle interprets the brain as continuously minimizing prediction-error ("surprise") – effectively reducing a variational free energy (KL divergence) to match its internal model to sensory input. Free energy minimization has been shown equivalent to classic Bayesian updating; thus cognition can be seen as a continuous drive to lower internal entropy by refining hypotheses. In short, brains seem to exploit physical laws to manage information flow and uncertainty.

Another angle comes from Maxwell's Demon thought experiments. Mizraji (2021) argues that biological systems implement "Maxwell's demons" at molecular and system levels: enzymes, receptors, and neural circuits actively select and direct information to maintain order far from equilibrium. These "biological Maxwell's demons" act as information catalysts, using sensory inputs to create and preserve structure (low entropy) in the organism. This suggests a cognitive negentropy law: intelligent agents will use information processing to locally reduce entropy or at least prevent its uncontrolled increase in their domain. Indeed, Szweizer & Schlagbaum's entropy-based model of cognition shows that information can self-organize into attractors (representing memory, beliefs, decisions) even without a subject, indicating that information itself can exhibit order and entropy dynamics akin to physical matter. In sum, cognitive systems both follow and bend thermodynamic rules by using information to shape their own "entropic" landscape.

At the neural level, these laws manifest in brain networks. Thermodynamic analyses of neural data show that different tasks alter the brain's entropy and irreversibility: for instance, task-related networks often produce higher "entropy production" (less reversibility) than rest. In the MnemoVerse formalism, such processes occur on the curved manifold where activation diffusion (analogous to heat flow) and attention-driven curvature determine how information spreads. The same mathematical tools (e.g. Laplace–Beltrami operators on , diffusion kernels, geodesic paths) used in Mnemoverse naturally connect to thermodynamics: diffusion equations govern memory fading, while entropy metrics quantify the irreversibility of trajectory flows in . Combining these insights suggests that cognition has its own entropy balance laws: memory formation, recall, and decision-making all correspond to transitions that must obey informational analogues of the first and second laws of thermodynamics.

2. Fundamental Laws of Cognitive Physics

Based on the above, we propose cognitive thermodynamic laws akin to physics:

2.1 Cognitive Second Law

Cognitive systems tend to minimize entropy (or at least its growth) within their sphere of influence. Through selective attention and information processing, intelligent agents act like Maxwell's demons, using data to locally reduce disorder. For example, learning and memory formation extract patterns (low-entropy structure) from sensory input, effectively exporting entropy to the environment (as heat, noise, or forgotten details).

2.2 Arrow-of-Time Principle

Mental processes are irreversible and directional. The brain exhibits a clear "arrow of time": information flows have a preferred direction, breaking time-reversal symmetry. Experimentally, non-equilibrium measures (like entropy production or asymmetry) increase during cognitive tasks relative to rest. Thus cognitive dynamics must satisfy an analogue of entropy production: the mental entropy never decreases for a closed cognitive system (free processing), consistent with a generalized second law.

2.3 Free-Energy Minimization

The brain continually minimizes a free-energy functional, aligning internal representations with incoming data. Formally, cognitive systems adjust , , and to reduce prediction errors, akin to a thermodynamic system relaxing towards equilibrium. This corresponds to minimizing a KL-divergence or "surprise" – effectively steering the system towards high-probability (low "energetic cost") states. In MnemoVerse, this could manifest as adjusting the activation field and metric to focus on expected concepts, thereby flattening free-energy landscapes.

2.4 Information Conservation (Landauer's Principle)

Any loss of cognitive information (e.g. forgetting) has an energetic cost. Erasing a bit of memory necessarily increases entropy and dissipates energy (Landauer's principle), even in neural terms. Deli et al. point out that positive vs. negative cognitive cycles have different thermodynamic costs. Thus MnemoVerse agents must account for the energy-entropy tradeoff of memory operations: efficient cognitive operations will seek reversible (lossless) transformations whenever possible.

2.5 Hierarchical Organization

Cognitive thermodynamics respects the manifold's geometry. In MnemoVerse, hierarchical coherence and context curvature are axioms. Thermodynamically, this implies that cognition naturally creates multiscale structure: detailed "cold" memory states and high-level "hot" abstractions emerge from diffusion-like heat kernels. Attention (analogous to temperature) dynamically reshapes this hierarchy – a hot, focused mind tightens the metric around relevant concepts, while a diffuse, unfocused mind flattens the geometry (increasing entropy). This matches observations: a well-focused cognitive state has low informational entropy, whereas distracted or random thought (high entropy) corresponds to a more uniform activation field.

Each of these laws connects to known models or findings. For example, Kringelbach & Deco's framework finds that brain entropy and hierarchy shift between conditions, consistent with these principles. Likewise, the field-equation model of cognition by Leizerman (2025) formalizes memory as a fractional field, inherently obeying conservation and causality constraints. Although such laws are speculative, the literature supports their plausibility: brains behave like non-equilibrium thermodynamic systems that organize information to temporarily beat entropy locally.

3. Mission Statement

Mnemoverse 2.0 is a GPU-native cognitive engine whose single governing objective is to minimise (or, at worst, stabilise) the entropy of its cognitive scene while continually ingesting new data, tasks and agent interactions.

This document unifies three threads discussed so far—thermodynamic principles, GPU scene representation, and hyperbolic (Poincaré) embeddings—into one coherent theory of Cognitive Thermodynamics.

4. Formal Definition of the Cognitive Scene

Level	Logical Entity	GPU Primitive	Notes
V	MNode — concept/fact with metadata & 5‑D position	struct { float4 pA; float pB; … }	Poincaré‑5D position
E	Semantic / syntactic edge	uint32[2] + weight	Index/element buffer
α	Attention distribution	3‑D float texture	Updated by compute shader
C	Context frame	Push constants ≤ 4 kB	Active window for an agent

Scene = 〈 G = (V,E), α, C 〉 where entropy
S = H(V) + H(E) – I(V;E) – Σ α(v) log α(v).

5. Six Laws of Cognitive Thermodynamics ⇄ Scene Mechanics

№	Law	Scene‑Level Implementation	Physical Analogue
1	Landauer‑Schrödinger
Q ≥ kT ln 2 · ΔN	Track E_erase for all delete/overwrite ops	Heat (Q)
2	Hierarchical σ
σ = KL(P₍fwd₎‖P₍rev₎)	TENET pass on event logs → σ heat‑map	Entropy production / arrow of time
3	Predictive Free Energy
F = Eₛᵤᵣₚ + β I(z;x)	β‑Scheduler tunes compression vs. surprise	Free energy (Helmholtz)
4	Catalytic Re‑use	Catalytic Linker searches a "family" before inserting node	Enzyme lowering ΔG‡
5	Critical λ ≈ 1	Chaos‑Guard PID regulates dropout/noise	Edge‑of‑chaos criticality
6	Night‑Time Anneal	Night‑Shift Daemon: batched delta‑compress + BVH rebuild	Thermal annealing / SHY

6. Why a Poincaré (Hyperbolic) Space?

• Exponential capacity: volume grows ~e^(d·r), so deep hierarchies embed with low distortion.
• Stable locality: negative curvature provides a built‑in margin; local updates don't perturb distant nodes.
• GPU‑friendly distance: one dot + one acosh per comparison → warp‑efficient k‑NN.

Recommended Dimensionality

d	VRAM per 10 M nodes	Mean distortion*	Use case
3	120 MB	~12 %	Visual debugging
5	200 MB	6–8 %	MVP (WordNet‑scale)
8	320 MB	< 5 %	Global ontologies

*Distortion = tree‑reconstruction error

7. Integrated Compute Chain (per frame)

graph LR
Q[Agent Query] -->|CPU→GPU| KNN[k‑NN on Poincaré SSBO]
KNN --> ATT[Attention texture α++]
ATT --> WALK[Edge‑walker shader]
WALK -->|≤32 KB| CPU[LLM / Planner]

Night‑Shift runs low‑priority, enforcing Law 6.

8. Instrumentation Dashboard

Metric	GPU Pass	Frequency
σ heat‑map	Mini‑TENET batch	10 s
λ	FFT on attention spikes	Real‑time
E₍erase₎	Bit‑counter · kT ln 2	Per‑frame
δ̄ (embedding distortion)	HS‑DTE on 1 % nodes	Nightly

9. Roadmap (6 months)

1. M1 — Entropy Dashboard (σ, λ, E₍erase₎).
2. M2 — Poincaré‑5D embedding + k‑NN shader; integrate β‑Scheduler.
3. M3 — Catalytic Linker & Chaos‑Guard ⇒ λ ∈ [0.8, 1.2].
4. Q2 — Night‑Shift Daemon; local curvature adaptation.
5. Q3 — Scale to 10⁷ nodes with flat global S.

10. Conclusion and Outlook

In summary, we propose that cognitive systems obey thermodynamic-like laws in an abstract information space. Cognition can be modeled as physics in the MnemoVerse's geometric framework: semantics are points in a curved manifold, attention and memory follow diffusion dynamics, and learning emerges as energy-efficient pattern extraction. Just as birds and planes both obey aerodynamics while being structurally different, biological and artificial cognition share these underlying physical constraints.

To develop this into a full theory, we will expand the mathematical derivations (e.g. using the Mnemoverse axioms and potentially a "PhisiX" system) and seek quantitative predictions (e.g. memory capacity limits or task-entropy laws). The cited works offer starting points: entropy production measures in neural data, free-energy formulations of inference, and Maxwell's demon models in biology. Our hope is that, by formalizing these intuitions, we can create a cognitive physics that guides the design of MnemoVerse's memory engine, yielding machines that organize and preserve information as efficiently as living minds. The depth and elegance of this idea – that mind and matter follow one set of informational laws – is indeed inspiring, and we will refine this hypothesis with further theoretical and empirical work.

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Status: Active development
Next Steps: Mathematical formalization and computational modeling
Collaboration: Open to researchers interested in consciousness theory and cognitive modeling

Glossary

• MNode — a knowledge vertex (concept/fact).
• σ — entropy production / irreversibility.
• β — "temperature of precision" in FEP.
• λ — largest Lyapunov exponent ≈ criticality.
• E₍erase₎ — energy cost of memory mutation.

References

1. Kringelbach M. L., Sanz Perl Y., & Deco G. (2024). The Thermodynamics of Mind. Trends in Cognitive Sciences, 28(6), 568–581. https://doi.org/10.1016/j.tics.2024.03.009
2. Deco G., Cruzat J., Sanz Perl Y., Tagliazucchi E., & Kringelbach M. L. (2023). The arrow of time of brain signals in cognition. Network Neuroscience, 7(3), 966–998. https://doi.org/10.1162/netn_a_00300
3. Deli E. K., Peters J. F., & Kisvárday Z. (2021). The thermodynamics of cognition: A mathematical treatment. Computational and Structural Biotechnology Journal, 19, 784–793. https://doi.org/10.1016/j.csbj.2021.01.008
4. Friston K. et al. (2023). The free energy principle made simpler but not too simple. Physics Reports, 1024, 1–29. https://doi.org/10.1016/j.physrep.2023.07.001
5. Mizraji E. (2021). The biological Maxwell's demons: Information processing in biological systems. Theory in Biosciences, 140(3), 307–318. https://doi.org/10.1007/s12064-021-00354-6
6. Szweizer M., & Schlagbaum R. (2021). Entropy‑based model for cognitive systems. OSF Preprints. https://doi.org/10.31219/osf.io/2tv9j
7. Leizerman S. (2025). Fractional‑Derivative Field Theory of Cognitive Memory. SSRN Working Paper. https://doi.org/10.2139/ssrn.5312123

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"Preserved entropy is earned time to learn." — MnemoVerse core principle

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