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Thermochemical Studies of Ni(II) and Zn(II) Ternary Complexes Using Ion Mobility-Mass Spectrometry

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Nonequilibrium tricritical point in a system with long-range interactions.

Andrea Antoniazzi¹, Duccio Fanelli, Stefano Ruffo

¹Dipartimento di Energetica and CSDC, Università di Firenze, and INFN, via S. Marta, 3, 50139 Firenze, Italy.

Physical Review Letters

|August 7, 2007

Summary

Systems with long-range interactions exhibit relaxation towards quasistationary states. A maximum entropy principle predicts phase transitions between homogeneous and inhomogeneous states, with metastability observed near first-order transitions.

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Area of Science:

Statistical Mechanics
Non-equilibrium Physics
Complex Systems

Background:

Systems with long-range interactions relax to quasistationary states.
State lifetime scales with system size.

Purpose of the Study:

Predict phase transitions in out-of-equilibrium systems.
Investigate relaxation dynamics in the Hamiltonian mean field model.
Explore the role of initial conditions in determining final states.

Main Methods:

Application of a maximum entropy principle.
Utilizing Lynden-Bell's concept of 'violent relaxation'.
Analysis of the Hamiltonian mean field model with 'water bag' initial conditions.

Main Results:

Prediction of out-of-equilibrium phase transitions.
Identification of transitions to homogeneous (zero magnetization) or inhomogeneous (non-zero magnetization) quasistationary states.
Discovery of first- and second-order phase transition lines merging at a tricritical point.
Theoretical prediction and numerical verification of metastability.

Conclusions:

Maximum entropy principle successfully predicts phase transitions in non-equilibrium systems.
Initial conditions dictate relaxation pathways towards different quasistationary states.
The study reveals complex phase behavior, including tricriticality and metastability, in systems with long-range interactions.