Scientific Results

Geometrical Aspects in the Analysis of Microcanonical Phase-Transitions

Year: 2020

Authors: Bel-Hadj-Aissa G., Gori M., Penna V., Pettini G., Franzosi R.

Autors Affiliation: DSFTA, University of Siena, Via Roma 56, 53100 Siena, Italy
Quantum Biology Lab, Howard University, 2400 6th St NW, Washington, DC 20059, USA
Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy Dipartimento di Fisica Università di Firenze, and I.N.F.N., Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
QSTAR & CNR – Istituto Nazionale di Ottica, Largo Enrico Fermi 2, I-50125 Firenze, Italy

Abstract: Inthepresentwork,wediscusshowthefunctionalformofthermodynamicobservablescan 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 φ4 models with either nearest-neighbours and mean-field interactions.

Journal/Review: ENTROPY

Volume: 22      Pages from: 380-1  to: 380-19

KeyWords: Statistical mechanics, microcanonical ensemble, entropy
DOI: 10.3390/e22040380