Related Experiment Video
Updated: Apr 1, 2026
06:44
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
689
Cycles, randomness, and transport from chaotic dynamics to stochastic processes.
1Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium.
Chaos (Woodbury, N.Y.)
|October 3, 2015
Summary
Dynamical systems theory reveals how initial condition sensitivity creates temporal disorder in deterministic systems. This disorder links to transport coefficients and breaks time-reversal symmetry in nonequilibrium statistical mechanics.
Area of Science:
- Physics, Applied Mathematics
Background:
- Deterministic dynamical systems can exhibit randomness due to sensitivity to initial conditions.
- Nonequilibrium statistical mechanics studies systems not in thermal equilibrium.
Purpose of the Study:
- To provide an overview of advances at the intersection of dynamical systems theory and nonequilibrium statistical mechanics.
- To explore the relationship between dynamical chaos and transport phenomena.
- To investigate the breaking of microscopic time-reversal symmetry in nonequilibrium systems.
Main Methods:
- Utilizing concepts from dynamical systems theory.
- Analyzing spatially extended systems with transport processes (e.g., diffusion).
- Applying methods to demonstrate the statistical-level breaking of time-reversal symmetry.
Main Results:
- Sensitivity to initial conditions is identified as a source of temporal disorder in deterministic systems.
- Relationships are established between dynamical chaos quantities and transport coefficients.
- Thermodynamic entropy production is linked to temporal disorder and time asymmetry away from equilibrium.
Conclusions:
- Dynamical systems theory offers new insights into the second law of thermodynamics.
- Microscopic time-reversal symmetry is broken at the statistical level in nonequilibrium systems.
- Temporal disorder is fundamentally related to entropy production and time asymmetry in nonequilibrium processes.
Related Concept Videos
01:10Entropy Change in Reversible Processes
3.4K
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.
3.4K
01:14The Second Law of Thermodynamics
7.2K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
7.2K
01:14The Entropy as a State Function
99
Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
99
02:49Second Law of Thermodynamics
28.5K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
28.5K
01:21Entropy Changes Accompanying Specific Processes
103
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...
103
02:39Entropy
38.0K
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...
38.0K