Onsager's variational principle in active soft matter

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 such as suspensions bacteria aggregates animal cells. We first extend general formulation dynamics where forces are included external non-conservative forces. then use analyze directional motion individual units: molecular motor walking on stiff biofilament toy two-sphere microswimmer. Next, we formulate diffuse-interface model an polar droplet solid substrate. addition generalized hydrodynamic equations fluids bulk region, have derived boundary conditions. Finally, consider thin under lubrication approximation. derive film equation employ approximation spreading laws droplet. By incorporating activity biological systems into OVP, develop approach construct models better understanding emergent behaviors cells cell or tissues.