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Related Concept Videos

Thermodynamic Systems01:06

Thermodynamic Systems

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A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
Consider an example of  tea boiling in a kettle. The...
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Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

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Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
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Mechanisms of Heat Transfer01:14

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Heat transfer between the human body and its environment occurs through four main mechanisms: conduction, convection, radiation, and evaporation.
Conduction, accounting for approximately 3% of body heat loss at rest, is the process of exchanging heat between molecules of two materials in direct contact. This can result in both heat loss and gain. For instance, when the body is submerged in water, which conducts heat 20 times more effectively than air, it can either lose or gain significant...
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Mechanisms of Heat Transfer I01:14

Mechanisms of Heat Transfer I

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Just as interesting as the effects of heat transfer on a system are the methods by which the heat transfer occur. Whenever there is a temperature difference, heat transfer occurs. It may occur rapidly, such as through a cooking pan, or slowly, such as through the walls of a picnic ice box. So many processes involve heat transfer that it is hard to imagine a situation where no heat transfer occurs. Yet, every heat transfer takes place by only three methods: conduction, convection, and radiation.
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Mechanisms of Heat Transfer II01:20

Mechanisms of Heat Transfer II

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In convection, thermal energy is carried by the large-scale flow of matter. Ocean currents and large-scale atmospheric circulation, which result from the buoyancy of warm air and water, transfer hot air from the tropics toward the poles and cold air from the poles toward the tropics. The Earth’s rotation interacts with those flows, causing the observed eastward flow of air in the temperate zones. Convection dominates heat transfer by air, and the amount of available space for the airflow...
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Thermal Sigmatropic Reactions: Overview01:16

Thermal Sigmatropic Reactions: Overview

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Sigmatropic rearrangements are a class of pericyclic reactions in which a σ bond migrates from one part of a π system to another. These are intramolecular rearrangements where the total number of σ and π bonds remain unchanged.
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Updated: Jan 7, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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ZENN: A thermodynamics-inspired computational framework for heterogeneous data-driven modeling.

Shun Wang1, Shun-Li Shang2, Zi-Kui Liu2

  • 1Department of Mathematics, Penn State University, University Park, PA 16802.

Proceedings of the National Academy of Sciences of the United States of America
|January 2, 2026
PubMed
Summary
This summary is machine-generated.

We introduce a zentropy-enhanced neural network (ZENN) for machine learning with heterogeneous data. ZENN improves generalization and robustness by learning energy and intrinsic entropy from diverse data sources.

Keywords:
classificationcritical phenomenadata-driven modelingnegative thermal expansionzentropy-enhanced neural network

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Area of Science:

  • Artificial Intelligence
  • Data Science
  • Machine Learning

Background:

  • Traditional entropy methods struggle with integrating heterogeneous datasets.
  • Growing data complexity necessitates advanced AI algorithms.
  • Existing models face challenges in capturing intrinsic data disparities.

Purpose of the Study:

  • To introduce a zentropy-enhanced neural network (ZENN) for effective learning from heterogeneous data.
  • To extend zentropy theory into data science for improved AI.
  • To enhance generalization and robustness in machine learning tasks.

Main Methods:

  • Developed a zentropy-enhanced neural network (ZENN) architecture.
  • Integrated intrinsic entropy and energy learning components.
  • Introduced a learnable temperature variable to model data heterogeneity.

Main Results:

  • ZENN demonstrated superior generalization and robustness on image and text classification tasks (CIFAR-10/100, BBC News, AG News).
  • Successfully reconstructed the Helmholtz energy landscape of Fe3Pt, capturing material behaviors like negative thermal expansion.
  • Outperformed state-of-the-art models in classification and energy landscape reconstruction.

Conclusions:

  • ZENN provides a versatile and robust framework for data-driven machine learning.
  • The zentropy-grounded approach is effective for scientific problems with complex, heterogeneous datasets.
  • ZENN advances AI capabilities in handling data uncertainty and physical disorder.