Related Experiment Video
Updated: May 17, 2026
10:08
Phase Behavior of Charged Vesicles Under Symmetric and Asymmetric Solution Conditions Monitored with Fluorescence Microscopy
Published on: October 24, 2017
Phase transitions and finite-size effects in integrable virial statistical models
Xin An1,2, Francesco Giglio3, Giulio Landolfi4
1Ghent University, Department of Physics and Astronomy, 9000 Ghent, Belgium.
Physical Review. E
|May 16, 2026
Summary
Thermodynamic models for finite systems are exactly solvable, revealing phase transitions as shock waves. This framework maps nuclear and quark matter phase diagrams, impacting the search for critical points.
Area of Science:
- Thermodynamics and Statistical Mechanics
- Condensed Matter Physics
- High-Energy Nuclear Physics
Background:
- Thermodynamic models often rely on approximations for complex fluid systems.
- Understanding phase transitions is crucial for describing matter under extreme conditions.
- Finite-size effects can significantly alter observable phenomena near critical points.
Purpose of the Study:
- To analyze exactly solvable thermodynamic models for finite-size fluid systems.
- To investigate the emergence of phase transitions and critical phenomena.
- To apply the framework to construct a quantum chromodynamics (QCD) phase diagram.
Main Methods:
- Utilizing a virial expansion of internal energy with respect to volume density.
- Solving nonlinear C-integrable partial differential equations (PDEs) for physical observables.
- Analyzing the thermodynamic limit (N→∞) and behavior near critical points.
Main Results:
- Demonstrated exact solvability of thermodynamic models for finite systems.
- Identified phase transitions as classical shock waves in the thermodynamic limit.
- Observed scaling behavior near critical points consistent with universality conjectures.
- Constructed a global QCD phase diagram, including nuclear and quark matter transitions.
- Highlighted the smearing effect of finite-size systems on critical signatures.
Conclusions:
- The developed framework provides an exact solution for thermodynamic models, offering insights into phase transitions.
- The study provides a novel approach to mapping QCD phase diagrams and understanding critical phenomena.
- Finite-size effects are critical considerations for experimental searches for the QCD critical point.
More Related Videos
Related Concept Videos
02:39Phase Transitions: Vaporization and Condensation
The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
02:31Phase 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...
01:21Phase 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...
01:10Entropy Change in Reversible Processes
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
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.
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.
01:25Transition State Theory
Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
02:39Phase 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...