Elsevier

Annals of Physics

Volume 214, Issue 1, 15 February 1992, Pages 180-218
Annals of Physics

Canonical ensembles from chaos II: Constrained dynamical systems

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Abstract

We present dynamical equations of motion to compute thermodynamic properties of constrained dynamical systems. In particular, we examine systems that can be described by generators of Lie algebras. In this method, additional (noncompact) degrees of freedom are added to the compact phase space to mock the effects of a heat bath. The equations of motion in this extended space are ergodic, and canonical ensemble averages reduce to time averages over the classical trajactory. We compute explicitly the thermodynamic properties of several simple systems, in particular, Hamiltonians with SU(2) and SU(3) symmetry.

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    Citation Excerpt :

    This is due to the particular structure of the spin equations of motion which are generated by the Casimir invariants of the underlying group on the same fundamental level as energy [14]. This leads to constrained dynamics in which conventional approaches based on extended systems fail [17]. Because the free classical spin equations of motion are derived from Hamiltonians written in terms of generators of a Lie algebra, constraints are the natural invariants of this algebra.

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Address after Sept. 1, 1991, Center for Theoretical Physics, Yale University, New Haven, CT 06511.

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