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We report on a study of the thermodynamics of the Ginzburg-Landau model fortwo-dimensional type-II superconductors near the transition from the normalstate to the Abrikosov-lattice state. We couch our analysis in terms of theparticipation-ratio entropy, $s(P)$, which expresses the volume inorder-parameter-space with a given participation-ratio for the local superfluiddensity. $s(P)$ completely determines the thermodynamics of the system. Wereport on results for $s(P)$ obtained analytically using perturbation expansionmethods and numerically using Monte Carlo simulation methods and discuss theweak first-order phase transition which occurs in this system in terms of theproperties of $s(P)$.Comment: 12 pages (RevTeX 3.0) and 2 figures, available upon request,  IUCM94-01

Participation-ratio entropy and critical fluctuations in the thermodynamics of pancake vortices