microcanonical ensemble; phase transitions; topological methods; Statistical and Nonlinear Physics; Statistics and Probability; Modeling and Simulation; Mathematical Physics; Physics and Astronomy (all); General Physics and Astronomy
Abstract :
[en] The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase transitions. In fact, in correspondence of a phase transition there are peculiar geometrical changes of the mechanical manifolds that are found to stem from changes of their topology. These findings, together with two theorems, have suggested that a topological theory of phase transitions can be formulated to go beyond the limits of the existing theories. Among other advantages, the new theory applies to phase transitions in small N systems (that is, at nanoscopic and mesoscopic scales), and in the absence of symmetry-breaking. However, the preliminary version of the theory was incomplete and still falsifiable by counterexamples. The present work provides a relevant leap forward leading to an accomplished development of the topological theory of phase transitions paving the way to further developments and applications of the theory that can be no longer hampered.
Disciplines :
Physics
Author, co-author :
GORI, Matteo ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS) ; Quantum Biology Lab, Howard University, Washington, United States
Franzosi, Roberto; DSFTA, University of Siena, Siena, Italy ; INFN Sezione di Perugia, Perugia, Italy ; QSTAR, CNR—Istituto Nazionale di Ottica, Firenze, Italy
Pettini, Giulio; Dipartimento di Fisica, Università di Firenze, I.N.F.N., Sezione di Firenze, Sesto Fiorentino, Italy ; Sezione di Firenze, INFN, Sesto Fiorentino, Italy
Pettini, Marco ; Aix-Marseille Univ, Université de Toulon, CNRS, Marseille, France ; CNRS, Centre de Physique Théorique, UMR7332, Marseille, France
External co-authors :
yes
Language :
English
Title :
Topological theory of phase transitions
Publication date :
16 September 2022
Journal title :
Journal of Physics. A, Mathematical and Theoretical
DARPA Aix-Marseille University Howard University Horizon 2020 Research and Innovation Programme
Funding text :
This work has been done within the framework of the project MOLINT which has received funding from the Excellence Initiative of Aix-Marseille University—AMidex, a French ‘Investissements d’Avenir’ programme. This work was also partially supported by the European Union’s Horizon 2020 Research and Innovation Programme under Grant Agreement No. 964203 (FET-Open LINkS project). Roberto Franzosi acknowledges support by the QuantERA ERA-NET Co-fund 731473 (Project Q-CLOCKS) and the support by the National Group of Mathematical Physics (GNFM-INdAM). Matteo Gori thanks the financial support of DARPA (USA) for his long term visit at Howard University at Washington D.C. during which part of this work was done. *
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