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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.

Photochemical Electrocyclic Reactions: Stereochemistry

Photochemical Electrocyclic Reactions: Stereochemistry

The absorption of UV–visible light by conjugated systems causes the promotion of an electron from the ground state to the excited state. Consequently, photochemical electrocyclic reactions proceed via the excited-state HOMO rather than the ground-state HOMO. Since the ground- and excited-state HOMOs have different symmetries, the stereochemical outcome of electrocyclic reactions depends on the mode of activation; i.e., thermal or photochemical.
Selection Rules: Photochemical Activation

Convolution Properties I

Convolution Properties I

Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:

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: Dec 22, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Study on an efficient hyper-chaos-based image encryption scheme using global bit permutation.

Jianfeng Zhang, Zhiying Lu, Min Li

Technology and Health Care : Official Journal of the European Society for Engineering and Medicine

|May 5, 2020

Summary

This study introduces a hyper-chaos and global bit cycle shift (HC-GBCS) image encryption method. It enhances security by altering pixel distribution, overcoming limitations of low-dimensional chaotic systems.

Keywords:

Hyper-chaos SHA-256 encryption global bit cycle shift

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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

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Last Updated: Dec 22, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Cryptography
Information Security
Applied Mathematics

Background:

Low-dimensional chaotic systems offer limited security compared to high-dimensional ones.
Traditional pixel-level permutations alter position but not intensity distribution.
Bit-level permutations can modify intensity distribution through intensive computation.

Purpose of the Study:

To present an efficient image encryption approach using hyper-chaos and global bit cycle shift (HC-GBCS).
To enhance image encryption security beyond conventional methods.

Main Methods:

Utilized SHA-256 secure hash algorithm to generate the initial key for the chaotic system.
Employed a 4D hyper-chaotic system to generate chaotic sequences.
Applied global bit permutation and a logistic map-extended chaotic series for diffusion.

Main Results:

The proposed HC-GBCS approach effectively encrypts images.
Demonstrated high security and stability in experimental analyses.
Confirmed the method's capability to alter pixel distribution.

Conclusions:

The HC-GBCS method addresses security issues in low-dimensional chaotic encryption.
Global bit permutation effectively transforms plain image pixel distribution, boosting cryptosystem security.