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A major point made on this website is that diagrams such as that above have little to do with thermodynamic entropy. Yet similar ones, e.g., card shuffling or mixed-up, different-colored sox, are commonly used as examples. However, thermodynamic entropy is intimately linked to energy, and any complete and meaningful picture of it must recognize this point.
What is energy? What is entropy?

The purpose of this website is to explain and illuminate energy and entropy, their history in the context of thermodynamics, and their applicability to real-world phenomena.

This is a new website, to which material will be added as it is developed. You can navigate through the site using the tabs in the top menu bar. As progress is made, more tabs will be added.

Initially, there are two main parts: Essays and Selected Publications. The Essays require less formal physics background and are intended for sophisticated lay persons, as well as science students and teachers at various levels. Much of the writing in the essays emphasizes ideas, and might serve as a conceptual aid for students and instructors of thermal physics courses. The Selected Publications are downloadable article reprints mainly for people who have gone at least through college-level introductory physics courses and have studied math through calculus. In addition there are Resources, namely, lists of scientific articles, books, and websites that contain subject matter of relevance to this website.

The Rationale for this Website

In what follows, I shall illustrate how the intimate connection of energy with entropy clearly surfaces in four distinct developments of thermodynamics and entropy. These were formulated, respectively, by Rudolf Clausius, Ludwig Boltzmann, Josiah Willard Gibbs, and Edwin T. Jaynes. In the Oxford English Dictionary, the subject of thermodynamics is defined as:
The theory of the relations between heat and mechanical energy, and of the conversion of either into the other.

All mechanical engineering students study thermodynamics, and typically learn about heat engines, of which automobile engines and electric power-generating plants are two examples. Engineering issues such as ways to design heat engines of higher efficiency have been, and continue to be, important in the development of the subject. In all of this, energy and entropy are central concepts.

Physicists tend to focus on ways to relate thermodynamics concepts to the microscopic behavior of molecules, while physical chemists are interested in the energetics of chemical reactions where two or more chemical compounds react with one another, generating a different set of compounds. In all such considerations, energy and entropy are closely-linked major issues.

The closest that common dictionary definitions get to the energy-entropy connection is that entropy is "a measure of the unavailability of its thermal energy for conversion into mechanical work." Unfortunately, this description is opaque to many readers and in particular, is not easily related to the formulations of thermodynamics by Rudolf Clausius, Ludwig Boltzmann, Josiah Willard Gibbs, and Edwin T. Jaynes, each of which is outlined in the

The close relationship between
internal energy and entropy, and the importance of internal energy in thermodynamics, coupled with the remarkable fact that none of the most common interpretations of entropy's "meaning" (other than the opaque one cited in the previous paragraph) address this, have inspired me to write All About Energy & Entropy.

Over many years, I have worked sporadically on a book about entropy. I composed outlines and filled in the details. In each case, when I left the topic for a while and returned to it, I was dissatisfied with what I had written. So, I am taking a different approach, namely, to write relatively brief—typically 2,000–4,000 words or so—largely self-contained essays about specific aspects of energy and entropy. I am hopeful that this will satisfy my desire to share my thoughts, hopefully helping others overcome the kinds of conceptual hurdles I encountered.

The material on this site will be updated as quickly as I am able to complete additional essays; i.e., this is a work in progress. To help get make the site useful to teachers early on, I've included relevant published articles by me, one of them (and a letter-to-the-editor) with my dear friend and energy-entropy enthusiast, Frank Lambert. I am grateful to him for encouraging me to share my thoughts on this topic.

You can tell when the site has been updated by the date at the bottom of each page. Please let me know of any reactions you have, be they positive or negative. I will be grateful for all feedback, especially suggestions for ways to improve the presentation. Thanks.

Harvey S. Leff
Professor Emeritus, California State Polytechnic University-Pomona
Visiting Scholar, Reed College 2010-2014
Portland, Oregon
September 2013

© 2013 Harvey S. Leff — Last updated: Thursday, 18 December 2014 05:24 AM