Liouville's Theorem and the canonical measure for nonconservative systems from contact geometry

Abstract

Standard statistical mechanics of conservative systems relies on the symplectic geometry of the phase space. This is exploited to derive Hamilton's equations, Liouville's theorem and to find the canonical invariant measure. In this work we analyze the statistical mechanics of a class of nonconservative systems stemming from contact geometry. In particular, we find out the generalized Hamilton's equations, Liouville's theorem and the microcanonical and canonical measures invariant under the contact flow. Remarkably, the latter measure has a power law density distribution with respect to the standard contact volume form. Finally, we argue on the several possible applications of our results.

arXiv comment8 pages, Theorem 1 added, it matches the published version

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Cited by in corpus (14)

• Contact Hamiltonian Mechanics
• Contact Hamiltonian Systems
• Contact Symmetries and Hamiltonian Thermodynamics
• A thermostat algorithm generating target ensembles
• Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread
• Dynamical Similarity
• Contact geometric descriptions of vector fields on dually flat spaces and their applications in electric circuit models and nonequilibrium statistical mechanics
• Legendre submanifolds in contact manifolds as attractors and geometric nonequilibrium thermodynamics
• A New Action for Cosmology
• Herglotz Action for Homogeneous Cosmology
• Invariant measures for some dissipative systems from the Jacobi last multiplier
• Phase space contraction rate for classical mixed states
• Equilibria and bifurcations in contact dynamics
• Jacobi Geometry and Hamiltonian Mechanics: the Unit-Free Approach