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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.

Entropy and the Second Law of Thermodynamics

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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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First Law Of Thermodynamics: Problem-Solving

First Law Of Thermodynamics: Problem-Solving

The first law of thermodynamics states that the change in internal energy of the system is equal to the net heat transfer into the system minus the net work done by the system. This equation is a generalized form of energy conservation and can be applied to any thermodynamic process.
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Propagation of Uncertainty from Random Error

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Cyclic Processes And Isolated Systems

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Related Experiment Video

Updated: May 24, 2025

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

Published on: June 15, 2018

Knowledge as a Breaking of Ergodicity.

Yang He¹, Vassiliy Lubchenko^2,3,4

¹Department of Chemistry, University of Houston, Houston, TX 77204 5003, U.S.A.

Neural Computation

|March 3, 2025

Summary

We developed a thermodynamic potential to train generative models. This approach creates multiple minima in the model

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Area of Science:

Statistical Mechanics
Machine Learning
Computational Physics

Background:

Generative models are crucial for complex data analysis.
Training generative models on large phase spaces is computationally challenging.
Understanding the energy landscape of generative models is key to their performance.

Purpose of the Study:

To develop a thermodynamic potential for guiding generative model training.
To investigate the emergence of multiple minima in generative models during training.
To analyze the relationship between training data, free energy, and model behavior.

Main Methods:

Constructing a thermodynamic potential for binary degrees of freedom.
Analyzing the free energy landscape of the generative model.
Investigating ergodicity breaking and its implications for learning and retrieval.

Main Results:

The thermodynamic potential guides training, leading to multiple free energy minima.
Ergodicity breaking in the training set separates it from a high-temperature phase.
Multiple minima can limit access to underrepresented patterns but improve functionality.

Conclusions:

Training generative models involves sampling a free energy surface with distinct bound states.
Ergodicity breaking is essential for model functionality but can hinder learning.
Employing multiple generative models, one per minimum, can mitigate learning and retrieval issues.