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Phase Transitions

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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 Transitions

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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...

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The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

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Related Experiment Video

Updated: Jun 21, 2026

All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics

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Published on: January 19, 2018

Discontinuous phase transitions of conserved threshold transfer process with deterministic hopping.

Sang-Gui Lee¹, Sang Bub Lee

¹Department of Physics, Kyungpook National University, Daegu 702-701, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 8, 2009

Summary

A new deterministic conserved threshold transfer process is proposed. This model exhibits a discontinuous, first-order phase transition across multiple dimensions, driven by site clustering.

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Area of Science:

Statistical Mechanics
Complex Systems Modeling

Background:

The conserved threshold transfer process is a model for particle dynamics.
Understanding phase transitions in such systems is crucial for various scientific fields.

Purpose of the Study:

To introduce and analyze a deterministic variant of the conserved threshold transfer process.
To investigate the critical behavior and dimensionality dependence of this new model.

Main Methods:

Development of the deterministic conserved threshold transfer process model.
Simulation and analysis of the model's critical behavior in 1, 2, and 4 dimensions.

Main Results:

The order parameter indicates a discontinuous, first-order phase transition.
This transition occurs consistently across all investigated dimensions (1, 2, and 4).
Analysis reveals that site clustering and critical site accumulation precede the steady state.

Conclusions:

The deterministic conserved threshold transfer process demonstrates first-order phase transitions.
Particle hopping determinism influences the nature of the phase transition.
Further investigation into the mechanisms of site clustering is warranted.