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

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An Informational Theoretical Approach to the Entropy of Liquids and Solutions.

Arieh Ben-Naim¹

¹Department of Physical Chemistry, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 9190401, Israel.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

Information theory, using Shannon's measure of information (SMI), offers a new way to understand the entropy of ideal gases and liquids. This approach interprets entropy as a measure of uncertainty about particle locations, extending to complex systems like water.

Keywords:

entropy information theory liquids solutions

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Area of Science:

Statistical Mechanics
Information Theory
Physical Chemistry

Background:

The statistical mechanical theory of liquids lags behind that of gases and solids.
Information theory has successfully derived the entropy of ideal gases using Shannon's measure of information (SMI).

Discussion:

This work extends the information-theoretic approach to derive and interpret the entropy of liquids and solutions.
Intermolecular interactions are incorporated as correlations, quantified by mutual information (MI).
This preserves the interpretation of entropy as a measure of uncertainty about particle locations.

Key Insights:

The lower entropy of liquids compared to gases is reinterpreted not as "order-disorder" but through SMI.
This information-theoretic framework provides a consistent interpretation across different phases, including the challenging liquid-gas transition.
It offers a clearer understanding of entropy in structured liquids like water and aqueous solutions.

Outlook:

The study paves the way for a unified information-theoretic understanding of entropy in various states of matter.
Further applications to complex liquids, heavy water, and solutions with solutes like argon and methane are discussed.