In this work we investigate Ricci flows of almost Kaehler structures on Lie
algebroids when the fundamental geometric objects are completely determined by
(semi) Riemannian metrics, or effective) regular generating Lagrange/ Finsler,
functions. There are constructed canonical almost symplectic connections for
which the geometric flows can be represented as gradient ones and characterized
by nonholonomic deformations of Grigory Perelman's functionals. The first goal
of this paper is to define such thermodynamical type values and derive almost
K\"ahler - Ricci geometric evolution equations. The second goal is to study how
fixed Lie algebroid, i.e. Ricci soliton, configurations can be constructed for
Riemannian manifolds and/or (co) tangent bundles endowed with nonholonomic
distributions modelling (generalized) Einstein or Finsler - Cartan spaces.
Finally, there are provided some examples of generic off-diagonal solutions for
Lie algebroid type Ricci solitons and (effective) Einstein and Lagrange-Finsler
algebroids.Comment: This version is accepted by Mediterranian J. Math. and modified
following editor/referee's requests. File latex2e 11pt generates 29 page
