Timing Inaccessibility and the Projection Bound: Resolving Maxwell's Demon for Continuous Biological Substrates

This paper asks whether continuous biological coupling can postpone some costs associated with irreversible record formation. It does not imply that all pre-output neural dynamics are reversible or that digital hardware pays the Landauer bound on every clock cycle.

The paper traces the Maxwell's demon lineage (Maxwell → Szilard → Landauer → Bennett) and asks how its bookkeeping changes for continuous substrates and path-degenerate dynamics. Landauer and Bennett did not require memory to be digitally implemented: the relevant issue is whether a physical protocol reduces logical alternatives, stabilizes a record, or resets memory. Structural correlations and written bits are both physical and must be analysed at the level of the actual operation.

Landauer's bound applies when a physical device performs a logically irreversible operation such as resetting a stabilized memory. The paper's two-stage model separates transient correlation from durable registration: the first stage need not incur a per-bit erasure bound, while the second may. Actual energy use still depends on coupling, noise, maintenance, error correction, and the implementation.