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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...
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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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Entropy and the Second Law of Thermodynamics01:20

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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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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
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The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...
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Machine-learning iterative calculation of entropy for physical systems.

Amit Nir1,2, Eran Sela1, Roy Beck3,2,4

  • 1The School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel.

Proceedings of the National Academy of Sciences of the United States of America
|November 20, 2020
PubMed
Summary
This summary is machine-generated.

We developed a machine-learning iterative calculation of entropy (MICE) method to accurately estimate system entropy. This approach overcomes limitations of current methods, offering a computationally efficient and general solution for complex systems.

Keywords:
entropy estimationjammingmachine learningmutual information

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Area of Science:

  • Computational Physics
  • Statistical Mechanics
  • Machine Learning Applications

Background:

  • Entropy characterization is vital for thermodynamics, phase transitions, and protein folding.
  • Existing entropy estimation methods are computationally expensive, lack generality, or are inaccurate for complex systems.

Purpose of the Study:

  • Introduce a novel, efficient, and accurate method for calculating system entropy.
  • Address the limitations of current entropy estimation techniques in computational physics.

Main Methods:

  • Developed machine-learning iterative calculation of entropy (MICE).
  • Iteratively divides systems into subsystems to estimate mutual information between pairs.
  • Employs flexible machine learning algorithms adaptable to system structures and symmetries.

Main Results:

  • Achieved state-of-the-art accuracy in calculating entropy for diverse thermal and athermal systems.
  • Successfully applied MICE to classical spin systems and identified the jamming point in soft disk mixtures.
  • Demonstrated the efficacy of mutual information as a diagnostic tool in physical system studies.

Conclusions:

  • MICE provides a powerful and versatile tool for entropy calculation in complex physical systems.
  • The method offers significant improvements in accuracy and computational efficiency over existing approaches.
  • Mutual information derived from MICE serves as a valuable diagnostic for understanding system behavior.