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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: 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...
Phase Diagram01:19

Phase Diagram

The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).

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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Temporal complexity of the order parameter at the phase transition.

Malgorzata Turalska1, Bruce J West, Paolo Grigolini

  • 1Center for Nonlinear Science, University of North Texas, Denton, Texas 76203-1427, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 30, 2011
PubMed
Summary

Criticality in decision-making models, equivalent to the Ising model, generates complex temporal fluctuations. This complexity matching is key for efficient information transfer between networks.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems Theory
  • Information Theory

Background:

  • Decision-making processes can exhibit complex behaviors.
  • Phase transitions in physical systems, like the Ising model, are associated with critical phenomena.
  • Complexity matching is a recent concept linking information transfer to shared temporal complexity.

Purpose of the Study:

  • To investigate the temporal complexity generated by a decision-making model at criticality.
  • To establish a link between criticality, temporal complexity, and information transfer.

Main Methods:

  • Modeling a decision-making process equivalent to the two-dimensional Ising model.
  • Analyzing the system's behavior at the onset of a phase transition.
  • Characterizing the generated fluctuations as nonstationary and nonergodic.

Main Results:

  • The decision-making model, at the phase transition's onset, exhibits nonstationary and nonergodic temporal fluctuations.
  • These fluctuations represent a form of temporal complexity inherent to criticality.
  • The findings support the principle of complexity matching for efficient information transfer.

Conclusions:

  • Criticality in decision-making models inherently generates temporal complexity.
  • Complexity matching provides a framework for understanding efficient information transfer in complex systems.
  • This research opens avenues for applying complexity matching in diverse fields involving information exchange.