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Global Optimization, The Gaussian Ensemble, And Universal Ensemble Equivalence., M Costeniuc, Rs Ellis, H Touchette, B Turkington
Global Optimization, The Gaussian Ensemble, And Universal Ensemble Equivalence., M Costeniuc, Rs Ellis, H Touchette, B Turkington
Mathematics and Statistics Department Faculty Publication Series
Given a constrained minimization problem, under what conditions does there exist a related, unconstrained
problem having the same minimum points? This basic question in global optimization
motivates this paper, which answers it from the viewpoint of statistical mechanics. In this context, it
reduces to the fundamental question of the equivalence and nonequivalence of ensembles, which is
analyzed using the theory of large deviations and the theory of convex functions.
In a 2000 paper appearing in the Journal of Statistical Physics, we gave necessary and sufficient
conditions for ensemble equivalence and nonequivalence in terms of support and concavity
properties of the …