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Related Concept Videos

Phase Transitions01:21

Phase Transitions

A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
Phase Transitions02:31

Phase Transitions

Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to occupy...
Entropy Changes Accompanying Specific Processes01:21

Entropy Changes Accompanying Specific Processes

Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression results...
The Phase Rule01:20

The Phase Rule

The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...
Phase Transitions: Sublimation and Deposition02:33

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Nonequilibrium phase transitions in systems with long-range interactions.

Tarcísio N Teles1, Fernanda P da C Benetti, Renato Pakter

  • 1Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, Rio Grande do Sul, Brazil.

Physical Review Letters
|February 2, 2013
PubMed
Summary
This summary is machine-generated.

We present a generalized Hamiltonian mean field model with explicit dynamics. This model reveals a nematic phase and highlights the limitations of Boltzmann-Gibbs statistics for long-range force systems.

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Last Updated: May 14, 2026

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Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Dynamical Systems

Background:

  • The standard Hamiltonian mean field (HMF) model, an XY model with long-range interactions, exhibits complex behavior.
  • Statistical mechanics, particularly Boltzmann-Gibbs statistics, is a cornerstone for understanding thermodynamic systems.
  • Understanding the interplay between dynamics and equilibrium statistical mechanics is crucial for complex systems.

Purpose of the Study:

  • Introduce a generalized HMF model with linear and quadratic spin couplings and explicit Hamiltonian dynamics.
  • Investigate the phase diagram of this generalized model, including paramagnetic, ferromagnetic, and a novel nematic phase.
  • Develop a dynamical theory to reconcile discrepancies between theoretical predictions and simulation results.

Main Methods:

  • Analytical solution of the generalized HMF model using Boltzmann-Gibbs statistical mechanics (canonical and microcanonical ensembles).
  • Molecular dynamics simulations to obtain the phase diagram.
  • Development of a dynamical theory to predict simulation-based phase diagrams.

Main Results:

  • The generalized HMF model exhibits paramagnetic, ferromagnetic, and nematic phases.
  • Significant differences were observed between the microcanonical phase diagram from statistical mechanics and that from molecular dynamics simulations.
  • A novel dynamical theory successfully predicts the molecular dynamics phase diagram without adjustable parameters.

Conclusions:

  • The generalized HMF model demonstrates the existence of a nematic phase.
  • Boltzmann-Gibbs statistics are inadequate for describing systems with long-range forces in the thermodynamic limit when dynamics are considered.
  • Explicit Hamiltonian dynamics play a fundamental role in determining the phase behavior of such systems.