Reference : Topology and Phase Transitions: A First Analytical Step towards the Definition of Suf...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Physics
Physics and Materials Science
Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions
di Cairano, Loris mailto [Forschungszentrum Jülich > Institute of Neuroscience and Medicine INM-9, and Institute for Advanced Simulation IAS-5 > > ; Aachen University > Department of Physics, Faculty of Mathematics, Computer Science and Natural Sciences]
Gori, Matteo mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS) >]
Pettini, Marco mailto [University of Aix-Marseille > > > ; Centre National de la Recherche Scientifique - CNRS > Centre de Physique Théorique UMR7332]
[en] Statistical Mechanics ; Phase Transitions ; Differential Geometry ; Microcanonical ensemble ; Topology
[en] Different arguments led to supposing that the deep origin of phase transitions has to be identified with suitable topological changes of potential related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of energy level submanifolds of the phase space. However, the sufficiency conditions are still a wide open question. In this study, a first important step forward was performed in this direction; in fact, a differential equation was worked out which describes how entropy varies as a function of total energy, and this variation is driven by the total energy dependence of a topology-related quantity of the relevant submanifolds of the phase space. Hence, general conditions can be in principle defined for topology-driven loss of differentiability of the entropy

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