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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.

Estimation of the Physical Quantities

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On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...

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.
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Entropy

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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...

Standard Entropy Change for a Reaction

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Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.

Random Error

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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...

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Low Complexity Estimation Method of Rényi Entropy for Ergodic Sources.

Young-Sik Kim¹

¹Department of Information and Communication Engineering, Chosun University, 309 Pilmoondae-ro Dong-gu, Gwangju 61452, Korea.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

We introduce a new method to estimate Rényi entropy, a generalized measure of randomness that includes Shannon entropy. This technique helps detect deviations in random data sources and is particularly useful for Rényi entropy of order 2.

Keywords:

Rényi entropy Shannon entropy entropy estimation nearest neighbor distance quadratic entropy random number generation security

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Area of Science:

Information Theory
Statistical Signal Processing
Randomness Measurement

Background:

Entropy is a key measure of randomness in data.
Existing methods focus on estimating various entropy types from random samples.
Rényi entropy generalizes Shannon entropy, offering a broader measure of randomness.

Purpose of the Study:

To propose a novel estimation method for Rényi entropy of order α.
To develop a technique capable of detecting significant deviations in ergodic stationary random sources.
To provide an estimation method applicable to generalized entropy measures.

Main Methods:

Development of a new estimation scheme for Rényi entropy.
Derivation of a general representation for the estimator's parameters.
Analysis of specific cases: α → 1, α = 1/2, and α = 2.
Presentation of an iterative estimation method for Rényi entropy of order 2.

Main Results:

The proposed estimation method is shown to be equivalent to the Rényi entropy of order α in expectation.
The method effectively detects deviations in random data sources.
An efficient iterative algorithm is provided for the commonly used Rényi entropy of order 2.

Conclusions:

The proposed method offers a robust way to estimate Rényi entropy.
This technique enhances the analysis of randomness in stationary data.
The iterative approach for order 2 entropy is suitable for resource-constrained applications.