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Entropy

Entropy

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...

Entropy

Entropy

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...

Entropy and the Second Law of Thermodynamics

Entropy 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...

Entropy and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...

The Entropy as a State Function

The 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...

Absolute Entropies and the Third Law of Thermodynamics

Absolute Entropies and the Third Law of Thermodynamics

Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing...

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Related Experiment Video

Updated: May 21, 2026

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Published on: June 27, 2013

Approximate entropy of network parameters.

James West¹, Lucas Lacasa, Simone Severini

¹Statistical Cancer Genomics, UCL Cancer Institute and Department of Physics & Astronomy, University College London, London, UK. jawest@gmail.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 12, 2012

Summary

This summary is machine-generated.

We introduce approximate entropy for network analysis, revealing its convergence to binary Shannon entropy in scale-free and Erdös-Rényi networks. This method distinguishes complex dynamical systems and has applications in cancer genomics.

Related Experiment Videos

Last Updated: May 21, 2026

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Published on: June 27, 2013

Area of Science:

Network Theory
Dynamical Systems
Information Theory

Background:

Approximate entropy quantifies uncertainty in time series and dynamical systems.
Network theory provides a framework for analyzing complex systems structure.
Existing methods lack robust measures for network-based dynamical complexity.

Purpose of the Study:

To adapt approximate entropy for network analysis.
To investigate structural and dynamical network properties using entropy.
To explore applications in dynamical systems and biological data.

Main Methods:

Computing approximate entropy on graph-derived sequences (slide sequence).
Analyzing scale-free and Erdös-Rényi networks.
Investigating approximate entropy on horizontal visibility graphs from time series.

Main Results:

A novel structural entropy measure converges to binary Shannon entropy for large networks.
Approximate entropy effectively distinguishes horizontal visibility graphs from processes with varying complexity.
The approach provides a dynamical perspective on network analysis.

Conclusions:

Approximate entropy is a versatile tool for network characterization.
This method enhances the study of complex systems and dynamical processes.
Potential applications exist in analyzing biological data, such as cancer genomics.