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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

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...

Second Law of Thermodynamics

Second Law of Thermodynamics

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...

Second Law of Thermodynamics

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. 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...

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 and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...

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Related Experiment Video

Updated: Apr 29, 2026

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

Maximum information entropy: a foundation for ecological theory.

John Harte¹, Erica A Newman¹

¹Energy and Resources Group, University of California at Berkeley, 310 Barrows Hall, Berkeley, CA 94720, USA; Department of Environmental Science, Policy, and Management, University of California at Berkeley, 130 Mulford Hall, Berkeley, CA 94720, USA.

Trends in Ecology & Evolution

|May 28, 2014

Summary

This summary is machine-generated.

The maximum information entropy (MaxEnt) principle accurately predicts ecological patterns like species-area relationships. This statistical method can form the basis for ecological theory and reveal driving mechanisms.

Keywords:

MaxEnt ecological theory information entropy macroecology maximum entropy theory of ecology

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Last Updated: Apr 29, 2026

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

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Published on: August 16, 2017

Experimental Protocol for Manipulating Plant-induced Soil Heterogeneity

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Published on: March 13, 2014

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

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Published on: July 30, 2019

Area of Science:

Ecology
Statistical Inference
Ecological Theory

Background:

The maximum information entropy (MaxEnt) principle is a robust statistical inference method.
MaxEnt has recently been applied to ecological studies.

Purpose of the Study:

To demonstrate MaxEnt's accuracy in predicting macroecological patterns.
To explore MaxEnt as a foundation for ecological theory.
To discuss how model-data mismatches can illuminate ecological mechanisms.

Main Methods:

Application of the maximum information entropy (MaxEnt) principle.
Analysis of species-area relationships (SARs).
Examination of abundance distributions.

Main Results:

MaxEnt accurately predicts species-area relationships.
MaxEnt accurately predicts abundance distributions.
The principle provides a foundation for ecological theory.

Conclusions:

MaxEnt is a powerful tool for ecological prediction and theory building.
Mismatches between MaxEnt predictions and data offer insights into ecological drivers.
Future extensions of the maximum entropy theory of ecology (METE) hold significant potential.