The entropy of Lagrange-Finsler spaces and Ricci flows

We formulate a statistical analogy of regular Lagrange mechanics and Finsler geometry derived from Grisha Perelman's functionals and generalized for nonholonomic Ricci flows. Explicit constructions are elaborated when nonholonomically constrained flows of Riemann metrics result in Finsler like configurations, and inversely, when geometric mechanics is modelled on Riemann spaces with a preferred nonholonomic frame structure.