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Related Concept Videos

Phase Transitions01:21

Phase Transitions

63
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...
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Phase Transitions02:31

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...
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Entropy Changes Accompanying Specific Processes01:21

Entropy Changes Accompanying Specific Processes

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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...
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Hindsight Biases01:12

Hindsight Biases

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Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Can you relate this to the phrase "Hindsight is 20/20" now? 
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Entropy Change in Reversible Processes01:10

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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.
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Critical Region, Critical Values and Significance Level01:16

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The critical region, critical value, and significance level are interdependent concepts crucial in hypothesis testing.
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Updated: Mar 29, 2026

Using Generative Art to Convey Past and Future Climate Transitions
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Using Generative Art to Convey Past and Future Climate Transitions

Published on: March 31, 2023

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Predictability of critical transitions.

Xiaozhu Zhang1, Christian Kuehn2, Sarah Hallerberg1

  • 1Network Dynamics, Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 15, 2015
PubMed
Summary

Critical transitions in systems may be predictable by observing "critical slowing down" indicators like increased variance. However, their statistical relevance as early warning signals for critical transitions is model-dependent and influenced by noise.

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Last Updated: Mar 29, 2026

Using Generative Art to Convey Past and Future Climate Transitions
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Area of Science:

  • Complex Systems Dynamics
  • Theoretical Physics
  • Mathematical Modeling

Background:

  • Critical transitions in multistable systems model diverse phenomena, including species extinctions, socioeconomic shifts, and climate change.
  • Bifurcation theory suggests critical transitions are preceded by 'critical slowing down,' observable as increased variance and autocorrelation.
  • The statistical relevance of these indicators, especially under noisy conditions, remains unclear for predicting critical transitions.

Purpose of the Study:

  • To investigate the predictability of critical transitions in conceptual models.
  • To analyze the statistical relevance and performance of potential early warning indicators.
  • To assess the influence of model specifics and transition magnitude on predictive success.

Main Methods:

  • Studied the quadratic integrate-and-fire model and the van der Pol model.
  • Introduced external noise to simulate realistic conditions.
  • Focused on statistical analysis of prediction success and system predictability using indicator variables.

Main Results:

  • The effectiveness of different indicator variables for predicting critical transitions varies significantly.
  • Predictive performance is dependent on the specific conceptual model being studied.
  • The conditions under which the system is accessed and the magnitude of transitions influence predictability.

Conclusions:

  • While critical slowing down indicators show promise, their reliability as universal early warning signals for critical transitions is context-dependent.
  • Further research is needed to refine prediction strategies across different systems and noise levels.
  • Understanding model-specific dynamics is crucial for accurately forecasting critical transitions.