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Entropy and Solvation02:05

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The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ...
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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 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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There are two criteria that favor, but do not guarantee, the spontaneous formation of a solution:
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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.
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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...
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Updated: Sep 18, 2025

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes
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Permutation Entropy and Its Niche in Hydrology: A Review.

Dragutin T Mihailović1

  • 1Department of Physics, Faculty of Sciences, University of Novi Sad Dositej Obradovic Sq. 3, 21000 Novi Sad, Serbia.

Entropy (Basel, Switzerland)
|June 26, 2025
PubMed
Summary

Permutation entropy (PE) quantifies time series complexity. This review highlights PE

Area of Science:

  • Hydrology and Complex Systems Analysis

Background:

  • Analyzing complexity in observational data often involves information measures applied to time series.
  • Permutation entropy (PE) quantifies time series disorder by examining value order relations.
  • PE is valued for its simplicity, robustness, and computational efficiency in complexity analysis.

Purpose of the Study:

  • To review the advantages and limitations of Permutation Entropy (PE).
  • To explore the diverse applications of PE in hydrology from 2002 to 2025.
  • To categorize PE's uses in various hydrological subfields.

Main Methods:

  • Review of scientific literature on Permutation Entropy applications in hydrology.
  • Categorization of PE usage across hydrological subfields.

Main Results:

Keywords:
AI based models in hydrologycomplex systemscomplexityhydrologypermutation entropytime series

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  • PE is a benchmark tool for complexity analysis due to its efficiency and robustness.
  • PE has been applied to runoff prediction, streamflow analysis, water level forecasting, hydrological change assessment, and infrastructure impact evaluation.
  • The review covers applications spanning from 2002 to 2025.

Conclusions:

  • Permutation Entropy effectively captures intricate dynamics in hydrological processes.
  • Leveraging PE enhances predictive models and deepens understanding of water-related phenomena.
  • PE offers a valuable approach for advancing hydrological research and applications.