Hamiltonian Dynamics as the Engine of Biological Computation

In the paper's words

This study investigates the physical basis of biological computation, focusing on the tension between static structuralism and dynamic evolution. Utilizing a Hamiltonian formulation of the Kuramoto model, we simulate a biological reservoir to rigorously evaluate the relationship between “Scale Inseparability” (coupling strength), Gamma oscillations (30-50 Hz), and computational utility. Our results demonstrate that biological Hamiltonian dynamics achieve superior dynamic stability and a 3.1x thermodynamic efficiency advantage over discrete digital baselines.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. Our preliminary analysis (see Section 4.5) suggests that Hamiltonian-governed biological models operate at approximately 32% of the activity-based metabolic cost of comparable digital baselines.

   from 1.4 Problem

2. In contrast, the Kuramoto reservoir, operating in the high-performance critical regime ($K=5.0$), operated at a cost of $\approx 16.1$—a 3.1x efficiency advantage (Milinkovic & Aru, 2025).

   from 4.5 Thermodynamic Cost

3. By leveraging the natural Hamiltonian evolution of the substrate, the Kuramoto reservoir achieved complex temporal dynamics at approximately 32% of the activity-based metabolic cost of the digital baseline (Section 4.5).

   from 6.3 The Energetic Price of

4. Finally, we supported H3 , revealing a 3.1x thermodynamic efficiency advantage for Hamiltonian dynamics over digital baselines, suggesting that “riding the physics” of the substrate is far cheaper than simulating it.

   from 7.1 Summary of Key Findings

How it is done

1. Utilizing a Hamiltonian formulation of the Kuramoto model, we simulate a biological reservoir to rigorously evaluate the relationship between “Scale Inseparability” (coupling strength), Gamma oscillations (30-50 Hz), and computational utility.

   from Abstract

2. In this biological paradigm, the “algorithm” is not a set of instructions executed on hardware, but rather the natural relaxation of the system’s energy landscape toward a stable minimum (Greydanus et al., 2019).

   from 1.1 The Static

3. This approach aligns with the principle of criticality , where the reservoir operates at the edge of chaos, balancing the order required for memory with the disorder required for separability (Wang et al., 2021).

   from 1.2 Biological

4. Objectives This study aims to formally validate Hamiltonian dynamics as the engine of biological computation, specifically linking the emergence of Gamma oscillations to stability and energy efficiency.

   from 1.5 Research Questions &

What would falsify it

1. Thus, “Gamma” is not merely a clock signal but the observable evidence of a Hamiltonian system operating at the edge of its stability basin, optimizing the trade-off between memory retention and input sensitivity.

   from 2.4 Criticality and the

2. This null result is not a failure of the system to retain information, but rather a demonstration of the fundamental difference in encoding schemes.

   from 5.1 Memory Capacity (MC)

3. Prediction Performance Our findings lend empirical support to McCaul’s hypothesis regarding feedback-free prediction in Hamiltonian reservoirs (McCaul et al., 2025).

   from 5.5 Feedback-Free

Where the claim stops

1. While we draw inspiration from neuroscience, we do not model specific biochemical processes (e.g., neurotransmitter diffusion) or wetware implementations.

   from 1.6 Scope & Delimitations

2. Furthermore, our investigation of “memory” is limited to the temporal retention of input signals (Jaeger’s Memory Capacity task) and does not extend to semantic or declarative memory types.

   from 1.6 Scope & Delimitations

3. Furthermore, the global coupling assumption used in our simulation is a simplification; biological brains use sparse, small-world topologies.

   from 6.6 Limitations of the

Where to read

1. Linking21 words · 1 min
2. Abstract145 words · 1 min
3. 1.0 Introduction1,189 words · 5 min
4. 2.0 Theoretical Framework1,196 words · 5 min
5. 3.0 Methodology906 words · 4 min
6. 4.0 Results I:1,150 words · 5 min
7. 5.0 Results II: Memory1,074 words · 5 min
8. 6.0 Discussion985 words · 4 min
9. 7.0 Conclusion & Future416 words · 2 min
10. Appendices898 words · 4 min