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Open AccessFeature PaperArticle

Geometrical Aspects in the Analysis of Microcanonical Phase-Transitions

1
DSFTA, University of Siena, Via Roma 56, 53100 Siena, Italy
2
Quantum Biology Lab, Howard University, 2400 6th St NW, Washington, DC 20059, USA
3
Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
4
Dipartimento di Fisica Università di Firenze, and I.N.F.N., Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
5
QSTAR & CNR - Istituto Nazionale di Ottica, Largo Enrico Fermi 2, I-50125 Firenze, Italy
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(4), 380; https://doi.org/10.3390/e22040380
Received: 5 February 2020 / Revised: 18 March 2020 / Accepted: 24 March 2020 / Published: 26 March 2020
(This article belongs to the Special Issue The Ubiquity of Entropy)
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the energy level sets of the Hamiltonian of a system under investigation. In particular, it turns out that peculiar behaviours of thermodynamic observables at a phase transition point are rooted in more fundamental changes of the geometry of the energy level sets in phase space. More specifically, we discuss how microcanonical and geometrical descriptions of phase-transitions are shaped in the special case of ϕ 4 models with either nearest-neighbours and mean-field interactions.
Keywords: microcanonical ensemble; phase transitions; differential geometry microcanonical ensemble; phase transitions; differential geometry
MDPI and ACS Style

Bel-Hadj-Aissa, G.; Gori, M.; Penna, V.; Pettini, G.; Franzosi, R. Geometrical Aspects in the Analysis of Microcanonical Phase-Transitions. Entropy 2020, 22, 380.

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