In this note, we provide a smooth variational principle on Wasserstein space by constructing gauge-type function using the sliced distance. This is crucial tool for optimization problems and in viscosity theory of PDEs space.

Onsager's variational principle (OVP) was originally proposed by Lars Onsager in 1931 [L. Onsager, $Phys. Rev.$, 1931, $37$, 405]. This fundamental provides a very powerful tool for formulating thermodynamically consistent models. It can also be employed to find approximate solutions, especially the study of soft matter dynamics. In this work, OVP is extended and applied dynamic modeling active...