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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 Change in Reversible Processes

Entropy 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 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...

Convolution: Math, Graphics, and Discrete Signals

Convolution: Math, Graphics, and Discrete Signals

In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...

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...

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Related Experiment Video

Updated: Jun 27, 2026

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

Published on: June 15, 2018

Complexity Entropy Analysis of Grid Chaotic System: Image Encryption and DSP Implementation.

Gang Hu¹, Baolin Kang¹, Xiaolin Ye²

¹School of Mathematics, Anshan Normal University, Anshan 114005, China.

Entropy (Basel, Switzerland)

|June 26, 2026

Summary

This summary is machine-generated.

Researchers used the Adomian decomposition method to create fractional-order differential equations, generating infinite attractors and fractal patterns. This led to a secure grid image encryption algorithm, merging chaos and fractals for new research avenues.

Keywords:

ADM Lyapunov exponent chaos complexity

Related Experiment Videos

Last Updated: Jun 27, 2026

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

Published on: June 15, 2018

Area of Science:

Mathematics
Chaos Theory
Fractal Dynamics

Background:

Fractional-order differential equations offer complex system dynamics.
Sine functions can introduce unique boosting effects in mathematical models.
Fractal geometry provides intricate patterns with self-similarity.

Purpose of the Study:

To construct true fractional-order differential equations using the Adomian decomposition method.
To explore the generation of infinite coexistence attractors and fractal patterns.
To develop a secure grid image encryption algorithm based on chaos and fractals.

Main Methods:

Application of the Adomian decomposition method (ADM).
Incorporation of a sine function for boosting effects.
Integration of fractal dynamics and chaos theory principles.

Main Results:

Successful construction of fractional-order differential equations.
Observation of infinite coexistence attractors on y-z planes.
Generation of grid fractal patterns, such as Koch snows.
Development of a highly secure grid image encryption algorithm.

Conclusions:

The study successfully combines chaos and fractals, opening new research directions.
The proposed encryption algorithm demonstrates enhanced security.
The grid effect, amplified by fractional order, is key to generating fractal patterns.