Special Issue "An Informational Theoretical Approach to the Entropy of Liquids and Solutions"
A special issue of Entropy (ISSN 1099-4300).
Deadline for manuscript submissions: closed (30 June 2019).
Interests: biochemistry; theory of liquids and solutions
Special Issues and Collections in MDPI journals
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Special Issue in Entropy: Entropy, the Second Law and Life
The statistical mechanical theory of liquids has been lagging far behind the theory of either gases or solids, Ben-Naim (2006). Recently, information theory has been used to derive and interpret the entropy of an ideal gas of simple particles (i.e., non-interacting and structure-less particles). Starting with Shannon’s measure of information (SMI) one can get the entropy function of an ideal gas, the same function derived in 1912 by Sackur and Tetrode.
The new deviation of the same entropy function, based on SMI, has several advantages listed in Ben-Naim (2008, 2017). Here we mention two: First, it provides a simple interpretation of the various terms in this entropy function. Second, and more important for our purpose, this derivation may be extended to any system of interacting particles including liquids and solutions, which is the central topic of this Special Issue of Entropy.
The main idea is that once one adds intermolecular interactions between the particles, one also adds correlations between the particles. These correlations may be cast in terms of mutual information (MI). Hence, we can start with the informational theoretical interpretation of the entropy of an ideal gas. Then, we add correction due to correlations in the form of MI between the locations of the particles. This process preserves the interpretation of the entropy of liquids and solutions in terms of a measure of information (or as an average uncertainty about the locations of the particles).
It is well-known that the entropy of liquids, any liquids for that matter, is lower than the entropy of a gas. This is manifested by the positive slope of the P(T) curve in the phase diagram of any substance. Traditionally, this fact is interpreted in terms of order–disorder; The lower entropy of the liquid is interpreted in terms of higher degree of order compared with that of the gas.
However, unlike in the case of transition from solid to either liquid, or to a gas phase where the order–disorder interpretation works well, the same interpretation would not work for the liquid-gas transition. It is hard, if not impossible to argue that the liquid is more “ordered” than the gaseous phase.
It is the purpose of this issue to examine some specific liquids, and compare their entropies with the extent of the intermolecular interactions between the molecules.
One outstanding liquid known to be a structured liquid, is water. This liquid will be discussed in a paper by Ben-Naim (this issue). In addition, heavy water, as well as aqueous solutions of simple solutes, such as argon or methane, will be discussed in this article.
Authors are invited to contribute, to this issue of Entropy, articles discussing the entropy of other liquids, of either pure substance or mixtures of different components.
Prof. Arieh Ben-Naim
Ben-Naim, A. (2006). A Molecular Theory of Solutions. Oxford University Press: Oxford, UK.
Ben-Naim, A. (2008). A Farewell to Entropy: Statistical Thermodynamics Based on Information. World Scientific: Singapore.
Ben-Naim, A. (2017). Information Theory, Part I: An Introduction to the Fundamental Concept. World Scientific: Singapore.
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- Information theory