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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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Entropy01:18

Entropy

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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.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
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Entropy and the Second Law of Thermodynamics01:20

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.
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...
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Second Law of Thermodynamics02:49

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. 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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Second Law of Thermodynamics00:53

Second Law of Thermodynamics

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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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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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Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes
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熱力学的エントロピー不確定性関係

Yoshihiko Hasegawa1, Tomohiro Nishiyama2

  • 1The University of Tokyo, Department of Information and Communication Engineering, Graduate School of Information Science and Technology, Tokyo 113-8656, Japan.

Physical review. E
|December 23, 2025
PubMed
まとめ
この要約は機械生成です。

この研究は、確率熱力学におけるシャノンエントロピーとエントロピー生成の間の定量的関係を確立する。意思決定モデルにおける決定精度とエントロピー生成の間の基本的なトレードオフを明らかにする。

キーワード:
確率熱力学情報理論統計力学不確定性関係エントロピー生成シャノンエントロピー意思決定

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Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
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科学分野:

  • 確率熱力学
  • 情報理論
  • 統計力学

背景:

  • 熱力学的不確定性関係は、観測量の精度とエントロピー生成を結びつける。
  • シャノンエントロピーは情報理論における不確実性を定量化する。
  • シャノンエントロピーとエントロピー生成の間の直接的な定量的関係は欠けている。

研究 の 目的:

  • 観測量のシャノンエントロピーとエントロピー生成の間の定量的関係を確立すること。
  • 観測量分布の非対称性を定量化するために対称性エントロピーを導入し、利用すること。
  • 確率的決定における基本的なトレードオフを実証すること。

主な方法:

  • シャノンエントロピーとエントロピー生成を用いた不確定性関係の定式化。
  • 分布の対称性を測定するための対称性エントロピーの導入。
  • 導出された関係を拡散決定モデルに適用すること。

主要な成果:

  • エントロピー生成と対称性エントロピーの合計の下限としてln2を確立した。
  • エントロピー生成とシャノンエントロピーの合計がln2以上であることを証明した。
  • 拡散モデルにおける決定精度とエントロピー生成の間のトレードオフを実証した。

結論:

  • シャノンエントロピーとエントロピー生成の間に基本的な不確定性関係が存在する。
  • 対称性エントロピーはエントロピー生成に関連する尺度を提供する。
  • この発見は、確率的決定プロセスを理解するための示唆を持つ。