Derive a broad many-body theorem suppressing thermodynamic return

Derive a broad many-body theorem that obtains both a positive spreading margin and asymptotic suppression of return-oriented current power from locality, transport, and record resolution.

Background

The paper develops an exact finite-step decomposition of the macrodistribution into a contribution generated by the macro-uniform representative and a residual generated by microscopic structure inaccessible to the current thermodynamic record. It further expresses the instantaneous entropy rate as a competition between entropy-spreading and return-oriented currents, and resolves the latter into energy-gap amplitudes.

Finite-system simulations show positive entropy-generation rates and no detectable distributional return during specified relaxation windows, while engineered commensurate dynamics can organize hidden microscopic information into macroscopic return. However, the paper does not establish a general theorem explaining when locality, transport properties, and the resolution of the thermodynamic record guarantee both suppression of return and a strictly positive entropy-spreading margin. The proposed problem seeks such a broad many-body result without extending the claim to universal all-time monotonicity or arbitrary systems.