Program
Research trajectory
Paper I constructs a reversible four-phase, single-ion mechanochemical transporter. Continuous position and momentum interact with conformational changes and maintained chemical reservoirs. Signed outside-edge events measure accomplished ion redistribution, while source caloric labels and mechanical energy distinguish functional transport from energy exchange.
The coupled generator gives an explicit obstruction to universal phase-only Markov dynamics. Two microscopic preparations can share the visible conformation and zero momentum while having different immediate outside-release rates. Complete observed phase histories instead determine a conditional measure over hidden mechanics, whose survival and event updates support source-faithful future prediction.
For the nominal positive-coupling model, robust rate envelopes and backward recursion give certified finite-window bounds on expected signed release and the probability of outside-edge events. A separate rare-history calculation encloses the conditional mean of initial energy. The four-phase graph yields an exact caloric path identity, while negative examples identify the information lost under coarse observation and some numerical approximations. The established Chinese medical distinction between qìjī (organized movement) and qìhuà (functional transformation) motivates the question without assigning a modern microscopic identity to qi.