Related Experiment Video
Updated: Jan 12, 2026
08:55
Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
8.9K
Emergent order from mixed chaos at low temperature
Pavel Chvykov1, Jeremy England2
1Institute for Globally Distributed Open Research and Education (IGDORE), Gothenburg, Sweden. pchvykov@igdore.org.
Scientific Reports
|November 4, 2025
Summary
Coupling chaotic Hamiltonian systems to a cold thermal bath reveals emergent regular behavior. This study quantifies order timescales and predicts transition temperatures, linking thermodynamics and dynamical systems.
Area of Science:
- Thermodynamics
- Dynamical Systems Theory
- Statistical Mechanics
Background:
- Hamiltonian systems with mixed phase space exhibit both regular and chaotic dynamics.
- Understanding emergent order in complex systems is a fundamental challenge.
- Connecting thermodynamic principles to dynamical system behavior remains an active research area.
Purpose of the Study:
- To explore the connection between thermodynamic and dynamical systems perspectives on emergent order.
- To provide evidence for the conjecture that Hamiltonian systems with mixed chaos spontaneously develop regular behavior when coupled to a thermal bath.
- To quantify the relationship between temperature, organization timescales, and the disruption of order.
Main Methods:
- Numerical simulations across five diverse dynamical systems.
- Analysis of phase-space contraction and thermal exploration.
- Derivation of transition temperatures based on relaxation timescales.
Main Results:
- Evidence supporting the conjecture that cold thermal baths induce regular behavior in chaotic Hamiltonian systems.
- Quantification of organization timescales and their temperature dependence.
- Prediction of transition temperatures, revealing a novel nonequilibrium fluctuation-dissipation relation.
Conclusions:
- Coupling to a cold thermal bath can lead to the emergence of robust dynamical order in complex systems.
- A formal connection is established between thermodynamic and dynamical systems viewpoints.
- Findings suggest a broad applicability to real-world systems where cold environments promote order.
Related Concept Videos
02:39Entropy
34.8K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
34.8K
01:18Entropy
3.5K
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
3.5K
01:22Entropy within the Cell
12.7K
A living cell's primary tasks of obtaining, transforming, and using energy to do work may seem simple. However, the second law of thermodynamics explains why these tasks are harder than they appear. None of the energy transfers in the universe are completely efficient. In every energy transfer, some amount of energy is lost in a form that is unusable. In most cases, this form is heat energy. Thermodynamically, heat energy is defined as the energy transferred from one system to another that...
12.7K
02:38Third Law of Thermodynamics
21.5K
A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
21.5K
02:39Phase Transitions: Melting and Freezing
14.5K
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...
14.5K
02:33Phase Transitions: Sublimation and Deposition
19.6K
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...
19.6K