Why it is a question
THEORY-026 holds, by a derivation in its dated note, that for a system driven without feedback the average work dissipated at a switch of the drive is kT times I[s_t;x_t] − I[s_t;x_{t+1}]. That nostalgia is nonnegative when the drive is Markov, by data processing on s_t – x_t – x_{t+1}. Summed over a protocol, it bounds the dissipation from below when each relaxation kernel keeps its equilibrium stationary, because relative entropy to that equilibrium then contracts.
The derivation uses each condition. It does not show that either is needed. A non-Markov drive lets a state that remembers x_{t−1} predict x_{t+1} better than it tracks x_t, which would make one step’s nostalgia negative. But the record has no kernel that keeps each equilibrium stationary and still holds that memory, so the failure is not exhibited. Until 2026-10-19 this, with a physical test, was THEORY-026’s promote_when.
What would answer it
- A fixed-kernel, feedback-free system, with each kernel keeping its equilibrium stationary and a non-Markov drive, in which one step’s nostalgia is negative or the summed nostalgia exceeds the dissipation. Or a proof that no such system exists.
- The same with a Markov drive and a kernel that does not keep its equilibrium stationary.
- A worked physical system in which measured dissipation tracks the nonpredictive information.
What would not answer it: results on systems with feedback. Those bear on THEORY-026’s scope, which is already limited, not on the bound.