Could a system consume energy even when everything you can see looks the same forwards and backwards in time?

Imagine watching a molecular switch that alternates between two visible states. Inside, there may be many hidden states. One tempting explanation is that a sufficiently complicated hidden mechanism could reproduce what you see while dissipating almost no energy.

This mathematical candidate shows exactly when that escape is possible, within a carefully specified class of stationary models. The complete waiting-time distributions must both be positive mixtures of exponential distributions. If they have that form, a finite reversible model exists. If not, adding more hidden states cannot make the minimum entropy-production rate approach zero.

The paper also turns a particular pattern in past and future waiting times into a numerical certificate. In one example, the certified floor is more than twice the earlier certificate for the same observations. This is a lower bound, not a measurement of the true minimum cost.

A second example passes a simple variance test for equilibrium but fails the full distribution test. It shows why the shape of the waiting-time law matters, not just its average or spread. A further result keeps the certificate positive when the observed probabilities lie inside a sufficiently small error box.

The research package includes the proofs, exact-arithmetic checks and code. It remains an unrefereed candidate. The assumptions exclude some important physical systems, and the paper does not provide a ready-made statistical confidence procedure for experimental data.

This is Evidence Press, Hidden dissipation without a known architecture, dated the third of October twenty twenty-six. The paper and evidence package are linked on the release page. This synthetic AI voice explains the research; it is not additional scientific evidence.