%0 Journal Article
%A Di Cairano, Loris
%A Gori, Matteo
%A Pettini, Marco
%T Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions
%J Entropy
%V 23
%N 11
%@ 1099-4300
%C Basel
%I MDPI
%M FZJ-2021-06112
%P 1414 -
%D 2021
%X 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.
%F PUB:(DE-HGF)16
%9 Journal Article
%$ pmid:34828112
%U <Go to ISI:>//WOS:000724133900001
%R 10.3390/e23111414
%U https://juser.fz-juelich.de/record/904542