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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...

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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...

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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Third Law of Thermodynamics

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Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Minimum Entropy Rate Simplification of Stochastic Processes.

Gustav Eje Henter, W Bastiaan Kleijn

IEEE Transactions on Pattern Analysis and Machine Intelligence

|March 2, 2016

Summary

We introduce Minimum Entropy Rate Simplification (MERS), a novel framework for simplifying generative models. MERS enhances model quality for sampling and enables nonparametric denoising of corrupted data.

Area of Science:

Information Theory
Stochastic Processes
Machine Learning

Background:

Generative models for stochastic processes often require simplification for improved performance.
Existing methods may not be parameterization-independent or suitable for denoising.
Model simplification is crucial for enhancing sampling quality and data cleaning.

Purpose of the Study:

To propose Minimum Entropy Rate Simplification (MERS), an information-theoretic framework.
To develop a parameterization-independent method for simplifying generative models.
To enable both model quality improvement for sampling and nonparametric denoising.

Main Methods:

Drawing on rate-distortion theory, MERS minimizes entropy rate under a dissimilarity constraint.

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Utilizing Kullback-Leibler divergence rate as the dissimilarity measure.

Deriving analytic solutions for Gaussian processes and Markov chains, applicable to maximum-entropy smoothing.

Main Results:

MERS effectively simplifies generative models across diverse domains.
The framework successfully denoises models from corrupted data.
Achieved improvements in model quality for sampling tasks by concentrating probability mass.

Conclusions:

MERS provides a robust and versatile approach to simplifying stochastic process models.
The method offers significant advantages in both model enhancement and data denoising.
Applicable to various fields including audio, text, speech, and meteorology.