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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...

The Entropy as a State Function

The Entropy as a State Function

Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...

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...

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...

Absolute Entropies and the Third Law of Thermodynamics

Absolute Entropies and the Third Law of Thermodynamics

Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing...

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Related Experiment Video

Updated: Jun 8, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Maximum entropy distributions of scale-invariant processes.

Veronica Nieves¹, Jingfeng Wang, Rafael L Bras

¹Department of Civil Environmental Engineering, University of California, Irvine, Irvine, California, USA. vnieves@uci.edu

Physical Review Letters

|September 28, 2010

Summary

The maximum entropy (ME) principle explains natural patterns without dominant scales, like soil moisture. This principle uses scale-invariant properties to predict probability distributions, offering a unified framework for multiscaling processes.

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Area of Science:

Environmental science
Statistical physics
Geosciences

Background:

Many natural variables, including soil moisture and topography, display complex organizational patterns lacking a single dominant scale.
Understanding these multiscaling phenomena is crucial for accurate environmental modeling and prediction.

Purpose of the Study:

To propose and demonstrate the utility of the maximum entropy (ME) principle for statistically describing scale-invariant natural variables.
To provide a unified theoretical framework for characterizing multiscaling processes observed in nature.

Main Methods:

Application of the maximum entropy (ME) principle to systems exhibiting scale-invariance.
Utilizing scale-invariant properties and the geometric mean for statistical description.
Relating probability distributions to macroscopic observables.

Main Results:

The ME principle successfully predicts the probability distribution of scale-invariant processes.
The framework offers a simple yet powerful method for analyzing complex natural patterns.
Demonstrates the universality of the ME principle in characterizing multiscaling phenomena.

Conclusions:

The maximum entropy (ME) principle provides a universal and unified approach to understanding and modeling natural variables with scale-invariant properties.
This statistical framework simplifies the characterization of complex, multiscaling systems in environmental and geoscientific contexts.