Related Experiment Video
Updated: Jun 24, 2026
11:15
Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
Published on: June 27, 2013
Control entropy: a complexity measure for nonstationary signals
Erik M Bollt1, Joseph D Skufca, Stephen J McGregor
1Clarkson University, P.O. Box 5815, Potsdam, NY 13699-5815, United States. bolltem@clarkson.edu
Mathematical Biosciences and Engineering : MBE
|March 19, 2009
Summary
We developed a new entropy statistic to track system changes using short time series data. This method can non-invasively assess physiological stress and monitor health status in real-time.
Area of Science:
- Complex Systems Analysis
- Physiological Monitoring
- Non-linear Dynamics
Background:
- Assessing slowly varying parameters in real systems often requires extensive data.
- Existing entropy measures may not be suitable for short or non-stationary time series.
- Understanding physiological constraints is crucial for health monitoring.
Purpose of the Study:
- To propose a novel entropy statistic for analyzing slowly varying parameters in short time series.
- To demonstrate the utility of this statistic in characterizing physiological time series.
- To explore its potential for non-invasive physiological stress assessment.
Main Methods:
- Developed an entropy statistic based on correlation entropy, symbol dynamics, and increment analysis.
- Applied a moving window approach to analyze entropy along time series.
- Validated the technique on physiological data, including power output during dynamic exercise.
Main Results:
- The entropy statistic effectively tracks the behavior of slow variables within a data series.
- The method achieves sufficient recurrence for entropy measurements on small datasets.
- Changes in signal entropy during dynamic exercise indicate alterations in underlying system constraints.
Conclusions:
- The proposed entropy statistic offers a robust method for analyzing complex systems with limited data.
- It provides a non-invasive and objective means to assess physiological stress under non-steady-state conditions.
- This technique holds promise for dynamic health status monitoring in various non-stationary systems.
More Related Videos
Related Concept Videos
02:39Entropy
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...
01:18Entropy
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...
01:14The Entropy as a State Function
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...
01:14The Second Law of Thermodynamics
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 put...
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.
01:20Entropy and the Second Law of Thermodynamics
The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...