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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.

Entropy Changes Accompanying Specific Processes

Entropy Changes Accompanying Specific Processes

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 results...

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...

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

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Related Experiment Video

Updated: Jun 26, 2026

Using Wavelet Entropy to Demonstrate how Mindfulness Practice Increases Coordination between Irregular Cerebral and Cardiac Activities

Using Wavelet Entropy to Demonstrate how Mindfulness Practice Increases Coordination between Irregular Cerebral and Cardiac Activities

Published on: May 10, 2017

Chaotic communication via temporal transfer entropy.

Yao-Chen Hung¹, Chin-Kun Hu

¹Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan.

Physical Review Letters

|December 31, 2008

Summary

This summary is machine-generated.

This study introduces a novel chaos communication method encoding binary messages into temporal relations of chaotic nodes. Information masked by noise can be recovered, showing robustness against attacks.

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Last Updated: Jun 26, 2026

Using Wavelet Entropy to Demonstrate how Mindfulness Practice Increases Coordination between Irregular Cerebral and Cardiac Activities

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Published on: May 10, 2017

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

Published on: June 27, 2013

Area of Science:

Complex Systems
Information Theory
Network Science

Background:

Traditional communication systems face challenges with noise and security.
Chaos theory offers complex dynamics that can be exploited for novel applications.

Purpose of the Study:

To propose and validate a new communication paradigm leveraging chaos theory.
To demonstrate robust information recovery in a noisy communication channel.

Main Methods:

Encoding binary messages into temporally causal relations within a coupled maps ring of N chaotic nodes.
Utilizing temporal transfer entropy for information recovery at the receiver.
Assessing the communication scheme's resilience against external noise and common attacks.

Main Results:

Successful encoding and decoding of binary messages using chaotic dynamics.
Demonstrated ability to recover masked information from transmitted signals.
Quantified robustness against simulated external noise and security threats.

Conclusions:

Chaos-based communication offers a viable and robust alternative to conventional methods.
Temporal transfer entropy is an effective tool for decoding information in chaotic communication systems.
The proposed scheme shows promise for secure and resilient data transmission.