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Related Concept Videos

Entropy02:39

Entropy

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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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Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

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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.
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The Second Law of Thermodynamics01:14

The Second Law of Thermodynamics

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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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Entropy within the Cell01:22

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A living cell's primary tasks of obtaining, transforming, and using energy to do work may seem simple. However, the second law of thermodynamics explains why these tasks are harder than they appear. None of the energy transfers in the universe are completely efficient. In every energy transfer, some amount of energy is lost in a form that is unusable. In most cases, this form is heat energy. Thermodynamically, heat energy is defined as the energy transferred from one system to another that...
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Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

2.8K
The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
2.8K
Second Law of Thermodynamics02:49

Second Law of Thermodynamics

23.8K
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...
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Entropy Production in a Fractal System with Diffusive Dynamics.

Rafael S Zola1, Ervin K Lenzi2, Luciano R da Silva3

  • 1Departmento de Física, Universidade Tecnológica Federal do Paraná-Campus de Apucarana, Apucarana 86812-460, PR, Brazil.

Entropy (Basel, Switzerland)
|December 23, 2023
PubMed
Summary
This summary is machine-generated.

This study explores entropy production in fractal systems using nonlinear Fokker-Planck equations. Anomalous diffusion and subsystem impacts on total entropy were demonstrated, highlighting fractal dynamics.

Keywords:
H-theorementropy productiongeneralized entropiesnonlinear diffusion

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Area of Science:

  • Statistical Mechanics
  • Complex Systems Theory
  • Fractal Geometry

Background:

  • Entropy production is a fundamental concept in thermodynamics and statistical mechanics.
  • Fractal systems exhibit complex structures and dynamics not captured by Euclidean geometry.
  • Nonlinear Fokker-Planck equations (NFEs) describe diffusion processes in various systems.

Purpose of the Study:

  • To investigate entropy production in a fractal system with two subsystems under external forces.
  • To analyze the impact of fractal geometry on diffusion dynamics and entropy.
  • To explore analytical and numerical solutions for the system's behavior.

Main Methods:

  • Application of the H-theorem to nonlinear Fokker-Planck equations.
  • Formulation of a general NFE using Hausdorff derivatives to incorporate fractal metrics.
  • Analytical and numerical investigation of system solutions.

Main Results:

  • Demonstrated that each subsystem influences the total entropy production.
  • Revealed anomalous diffusive processes due to the fractal nature of the system.
  • Quantified the effect of fractal geometry on entropy and diffusion.

Conclusions:

  • Fractal properties significantly alter diffusion dynamics and entropy production.
  • The interplay between subsystems is crucial for understanding total system entropy.
  • The developed NFE framework with Hausdorff derivatives is effective for fractal systems.