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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.
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Entropy

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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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Wald-Wolfowitz Runs Test II

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For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and...

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Efficient Approximations for Matrix-Based Rényi's Entropy on Sequential Data.

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|September 19, 2023

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Researchers developed a faster method to calculate matrix-based Rényi

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Area of Science:

Information Theory and Signal Processing
Computational Mathematics

Background:

Matrix-based Rényi's entropy (MBRE) offers direct data sample analysis, bypassing complex density estimation.
The computational expense of MBRE, particularly eigenvalue decomposition for sequential data, limits its large-scale application.
Existing MBRE methods face significant time complexity, scaling with the number and size of sliding windows.

Purpose of the Study:

To develop computationally efficient randomized approximations for MBRE.
To reduce the query complexity of MBRE estimation for large-scale and sequential data.
To maintain high accuracy while substantially improving computational speed.

Main Methods:

Utilized a static MBRE estimator combined with a variance reduction criterion.
Developed randomized approximation algorithms leveraging historical estimation results.
Employed polynomial approximation techniques for arbitrary entropy orders and analyzed convergence rates.

Main Results:

Achieved a significant reduction in computational complexity, particularly for sequential data analysis.
Demonstrated high accuracy with substantially lower query complexity compared to existing methods.
Validated effectiveness through large-scale simulations and real-world data experiments, showing promising speedup.

Conclusions:

The proposed randomized MBRE algorithms offer a computationally efficient alternative for large-scale applications.
These methods provide a practical solution for analyzing sequential data with reduced computational burden.
The approach achieves a favorable balance between computational speedup and minimal performance loss.