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The macroscopic Kaehler metric of Geometric Thermodynamics versus the microscopic one on the Event Manifold: Exact Partition Functions on CV manifolds. Extended Souriau temperatures and spontaneous magnetizations

arXiv:2606.09438v1 Announce Type: cross Abstract: In this paper we clarify the relation between Geometric Thermodynamics and Information Geometry based on the Fisher matrix. On the macroscopic odd-dimensional contact manifold of thermodynamic variables, we introduce for the first time a metric, whose pull-back on the isoentropic symplectic submanifolds transverse to the Reeb field is K\"ahlerian. The pull-back of such metric on equilibrium states, that are lagrangian submanifolds, is the...

arXiv CS 1d ago

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Mike Korostelev / GettyWaves crash over a Pacific walrus on a beach in Chukotka, Russia. humpback whale raises its tail before a deep-feeding dive, with the Port of Tacoma and Mount Rainier in the background. Wolfgang Kaehler / LightRocket / GettyA spirit bear (Ursus americanus kermodei) walks along a river looking for salmon on Gribbell Island, Great Bear Rainforest, British Columbia, Canada, on September 6, 2025.Naoki Haranaka / The Yomiuri Shimbun / ReutersSalmon, on their way to spawn,...

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