*Theorem on the origin of phase transitions*

**Year: ***2004*

**Authors: ***Franzosi R., Pettini M.*

**Autors Affiliation: **Dipartimento di Fisica, Università di Pisa, I.N.F.N., Sezione di Pisa, and I.N.F.M., Unità di Pisa, via Buonarroti 2, I-56127 Pisa, Italy; Istituto Nazionale di Astrofisica, Largo E. Fermi 5, 50125 Firenze, I.N.F.M., Unità di Firenze, and I.N.F.N., Sezione di Firenze, Italy

**Abstract: **For physical systems described by smooth, finite-range, and confining microscopic interaction potentials V with continuously varying coordinates, we announce and outline the proof of a theorem that establishes that, unless the equipotential hypersurfaces of configuration space Sigma(v)={(q(1),…,q(N))is an element ofR(N)\\V(q(1),…,q(N))=v}, vis an element ofR, change topology at some v(c) in a given interval [v(0),v(1)] of values v of V, the Helmoltz free energy must be at least twice differentiable in the corresponding interval of inverse temperature (beta(v(0)),beta(v(1))) also in the N–>infinity limit. Thus, the occurrence of a phase transition at some beta(c)=beta(v(c)) is necessarily the consequence of the loss of diffeomorphicity among the {Sigma(v)}(v

**Journal/Review: **PHYSICAL REVIEW LETTERS

**Volume: **92 (6) **Pages from: **060601-1 **to: **060601-4

**KeyWords:** Diffeomorphicity; Helmoltz free energy; Legendre transforms; Wave numbers, Computer simulation; Degrees of freedom (mechanics); Differentiation (calculus); Free energy; Hamiltonians; Kinetic energy; Lyapunov methods; Markov processes; Matrix algebra; Monte Carlo methods; Probability density function; Thermodynamics, Phase transitions**DOI: **10.1103/PhysRevLett.92.060601**ImpactFactor: **7.218**Citations: **94

data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-06

References taken from IsiWeb of Knowledge: (subscribers only)**Connecting to view paper tab on IsiWeb: **Click here**Connecting to view citations from IsiWeb: **Click here