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Entropy and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

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...

Entropy

Entropy

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...

Entropy

Entropy

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...

Entropy Change in Reversible Processes

Entropy Change in Reversible Processes

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.

The Second Law of Thermodynamics

The Second Law of Thermodynamics

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...

Gibbs Free Energy

Gibbs Free Energy

One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...

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Updated: Jan 8, 2026

Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions

Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions

Published on: January 30, 2018

有限データのための転移エントロピー

¹University of Hong Kong, University of Hong Kong, University of Hong Kong, Institute of Data Science, Hong Kong SAR, China; Department of Urban Planning and Design, Hong Kong SAR, China; and Urban Systems Institute, Hong Kong SAR, China.

Physical review. E

|December 23, 2025

まとめ

この要約は機械生成です。

この研究は、離散データのための新しい転移エントロピー尺度を導入し、小さいまたは高カーディナリティ時系列分析におけるバイアスと有意性の問題を克服します。シミュレーションなしで情報フローの信頼性の高い評価を可能にします。

キーワード:

転移エントロピー情報理論時系列分析複雑系ノンパラメトリック検定

さらに関連する動画

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Published on: June 27, 2013

関連する実験動画

Last Updated: Jan 8, 2026

Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions

Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions

Published on: January 30, 2018

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Published on: August 16, 2017

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Published on: June 27, 2013

科学分野:

複雑系分析
情報理論
時系列分析

背景:

転移エントロピーは、方向性のある情報フローを定量化しますが、連続データでは課題に直面します。
離散データの場合、疎なカウントによる正のバイアスに苦しみ、統計的有意性の評価が欠けています。
既存の方法は、小さいサイズまたは高いカーディナリティの有限データストリームでは苦労します。

研究の目的:

有限離散データストリームのための新しい転移エントロピー尺度を開発すること。
既存の推定値の限界、特にバイアスと有意性検定の欠如に対処すること。
シミュレーションに依存せずに、統計的有意性のノンパラメトリックな評価を可能にすること。

主な方法:

有限データストリームの情報量を計算することにより、新しい転移エントロピー尺度を導出しました。
シンボルを確率変数として明示的に考慮することを避けました。
標準的なプラグイン推定値との漸近的等価性を確保しました。

主要な成果:

新しい尺度は、標準的なプラグイン推定値と漸近的に同等です。
疎なビンカウントに関連する正のバイアスの問題を効果的に修正します。
有限時系列の統計的有意性の完全にノンパラメトリックな評価を可能にします。
この方法は、小さいサイズおよび/または高いカーディナリティの時系列に適しています。

結論:

提案された転移エントロピー尺度は、離散有限データの情報フローを分析するための堅牢なソリューションを提供します。
従来のメソッドの重大な制限を克服し、信頼性と解釈可能性を高めます。
複雑系における方向性のある情報転送の厳密な統計的検証を可能にします。