Timing inaccessibility and the projection bound: Resolving Maxwell’s demon for continuous biological substrates
Year: 2025
Type: article
Abstract: We show that the thermodynamic advantage of biological, continuous substrates over digital simulators arises from timing inaccessibility : below the Landauer threshold, temporal order cannot be irreversibly registered without dissipating ≥ k B T ln 2 per binary decision. Consequently, exponentially many micro-trajectories map to the same observable outcome ( path degeneracy ). Continuous high-dimensional substrates exploit this by integrating sub-Landauer couplings during evolution and paying only at projection (dimensional collapse to a low-dimensional output). We derive a Projection Bound for quasistatic projection at effective temperature T eff : (0.1) E collapse ≥ k B T eff ln N ɛ , pre N ɛ , post − KL p pre ∥ U pre + KL p post ∥ U post which reduces under typical-set conditions to E collapse ≥ k B T eff ln ( N ɛ , pre / N ɛ , post ) . Combined with a Temporal Registration Bound (order over M bins needs log 2 M ! bits), we quantify the gap: enumerative digital tracking scales exponentially with dimension, whereas projection cost scales like ln G ∼ D . For biologically plausible parameters, we estimate degeneracies of 1 0 42 – 1 0 94 (protein folding) and 1 0 50 – 1 0 100 (neural dynamics) as upper bounds under independence assumptions. The framework reconciles stochastic resonance (amplitude detection) with order inaccessibility, and clarifies why analog/neuromorphic systems gain efficiency by deferring projection.
Source: Biosystems
Author: Ian Todd
Institution: The University of Sydney
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,870
OpenAlex ID: W4415818906