Determine an exact power functional for Brownian dynamics

Develop an exact power functional for Brownian many-particle dynamics so that power functional theory can describe superadiabatic effects without relying on closure approximations.

Background

Power functional theory is presented as the dynamical counterpart of equilibrium density functional theory and, in principle, accounts exactly for superadiabatic contributions. Unlike equilibrium density functional theory, however, the exact power functional is not available, so practical calculations require analytical or machine-learned approximations. The absence of an exact functional motivates the development of improved first-principles or otherwise systematically controlled formulations.

References

Unlike the equilibrium case, however, no exact power functional is known, and the theory must be closed by an approximation.

— Superadiabatic Dynamical Density Functional Theory for One-Dimensional Brownian Hard-Rod Fluids  (2609.29838 - Weimar et al., 24 Sep 2026) in Introduction, paragraph beginning “Superadiabatic contributions are accounted for exactly by power functional theory”

An elegant solution would be to employ a canonical density functional. Subsequently, the inhomogeneous OZ equation could be replaced by its canonical counterpart without any further modifications. However, despite ongoing research , no applicable functional is known.

— Superadiabatic Dynamical Density Functional Theory for One-Dimensional Brownian Hard-Rod Fluids  (2609.29838 - Weimar et al., 24 Sep 2026) in Section 6, “Conclusion and Outlook,” paragraph beginning “An elegant solution would be to employ a canonical density functional”