Lagrange-Ricci Flows and Evolution of Geometric Mechanics and Analogous Gravity on Lie Algebroids

Details Lagrange-Ricci Flows and Evolution of Geometric Mechanics and Analogous Gravity on Lie Algebroids Lagrange-Ricci Flows and Evolution of Geometric Mechanics and Analogous Gravity on Lie Algebroids

2011-08-22

arxiv.org/abs/1108.4333v2

Physics

Mathematical Physics

latex2e, 11pt, 24 pages, v2 with typos corrected and modified list of references

Scientific paper

The approach to nonholonomic Ricci flows and geometric evolution of regular Lagrange systems [S. Vacaru: J. Math. Phys. 49 (2008) 043504 & Rep. Math. Phys. 63 (2009) 95] is extended to include geometric mechanics and gravity models on Lie algebroids. We prove that such evolution scenarios of geometric mechanics and analogous gravity can be modeled as gradient flows characterized by generalized Perelman functionals if an equivalent geometrization of Lagrange mechanics [J. Kern, Arch. Math. (Basel) 25 (1974) 438] is considered. The R. Hamilton equations on Lie algebroids describing Lagrange-Ricci flows are derived. Finally, we show that geometric evolution models on Lie algebroids is described by effective thermodynamical values derived from statistical functionals on prolongation Lie algebroids.

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