Entropy explained


Entropy, we are told, measures the tendency of a system to fall into disorder. This is a familiar concept, since culturally we speak of messiness (messy desks, messy rooms) as demonstrations of an increase in entropy.

But what we have all been taught is was wrong.  Thermodynamic entropy is not a measure of chaos. It is not a measure of the tendency of systems to fall into disorder and decay. The most current view of entropy states that entropy “measures the dispersal of energy: how much energy is spread out in a particular process, or how widely spread out it becomes.”

So how was the misconception of entropy as disorder born?

In the nineteenth century, the Austrian physicist Ludwig Boltzmann first described entropy as “disorder” in an attempt to aid the visualization of his theory of what molecules do spontaneously. Boltzmann’s innocent description is the foundation of a century of misunderstanding.

Why is a messy desk with towering to-do piles a poor example of an increase in entropy? Because towering to-do piles do not assemble themselves spontaneously, and entropy measures the spontaneous behavior of atoms and molecules. A change in entropy can be disorderly– a speeding car smashing into a brick wall — but entropy is not itself a measure of the increase in disorder. It’s a measure of energy spreading out, no matter how orderly or disorderly the fashion in which this happens.

Not all changes in entropy require an increase in disorder. When a heated chunk of metal radiates its heat into the surrounding environment, is that disorder? When you pour cream into coffee and the liquids spontaneously mix, is that disorder?

Boltzmann’s brilliant career shouldn’t be judged on this misstep, but nonetheless this piece of misinformation found its way into chemistry textbooks and classrooms everywhere.

Because textbook authors focused on Boltzmann’s good theory but still used his bad description, nearly every student in chemistry or physics in the last century has learned that entropy is disorder, or at least the tendency towards disorder. Boltzmann’s description stuck, and the misconception became part of chemistry classrooms for over a century.

But since 2002, when a retired chemistry professor questioned the error in a series of articles and saw his questioning take root in the educational community, the majority of new editions of General Chemistry texts have removed disorder in connection with entropy. Nowadays they use some variation on the idea that entropy measures the dispersal of energy.

Below are some changes in entropy represented as the dispersal of energy rather than the tendency to disorder (the following are adapted from the website Entropy Is Simple…):

Hot pans cool off

Water flows down Niagara Falls

Air in a tire will blow out into the atmosphere if the tire’s walls are punctured

When gasoline is mixed with air in a car’s cylinders, it reacts with oxygen if a spark is introduced

So what’s a good simple definition of entropy? Entropy is a measure, at a specific temperature, of all types of energy flows from the state of being localized to the state of being dispersed.

Here are some closing thoughts, again from Entropy Is Simple…:

Although order/disorder is still present in some elementary chemistry texts as a gimmick for guessing about entropy changes (and useful to experts in some areas of thermodynamics), it is both misleading and an anachronism for beginners in chemistry. It has been deleted from most first-year university chemistry textbooks in the U.S. In the humanities and popular literature, the repeated use of entropy in connection with “disorder” (in the multitude of its different common meanings) has caused enormous intellectual harm. Entropy has been thereby dissociated from the quintessential connection with its atomic/molecular energetic foundation.

The result is that a nineteenth century error about entropy’s meaning has been generally and mistakenly applied to disorderly parties, dysfunctional personal lives, and even disruptions in international events. This may make pages of metaphor but it is totally unrelated to thermodynamic entropy in physico-chemical science that actually does impact our lives.

For an overview of thermodynamic entropy and the fascinating Second Law of Thermodynamics, check out Entropy Is Simple…

Articles for students and educators on the subject of entropy can be found at entropysite.com.

Thanks to the Polish website ENTROPIA for the image that appears in this post.

12 responses to “Entropy explained

  1. It was really an eye opener. I always read entropy as ‘disorder’ in the universe that can not return to its original form. But looking at this concept from the new angle has really amazed me with joy !! Now it is really possible to imagine it in physical world as any other entity. Thanks a lot dear for the information.

  2. In my view.

    Entropy is the measurement of energy which is minus the calulation of the proposed output of an eficient engine.


  3. Hello Jennifer, like your blog. I am a sculptor researching ideas around entropic states. I was particularly drawn to the image at the top of the page the cloud-like form. I wonder if you could tell me where is it from and what is it? Mat

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  6. Ray Eston Smith Jr

    You’ve been conned. The Wikipedia article you read is probably one of several that have been hijacked by Frank Lambert. He is a liar. He lists books that he claims he has influenced but, strangely, not a single quote from a single author acknowledging that influence.

    Read up on Boltzmann. He was one of the greatest scientists of all time, but he was driven to suicide by idiots like Lambert. Here’s an extract from the wikipedia article on Boltzmann: (http://en.wikipedia.org/wiki/Boltzman)
    In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. She was refused permission to unofficially audit lectures, and Boltzmann advised her to appeal; she did, successfully. ….Boltzmann spent a great deal of effort in his final years defending his theories…Georg Helm and Wilhelm Ostwald presented their position on Energetics, at a meeting in Lübeck in 1895. They saw energy, and not matter, as the chief component of the universe. However, Boltzmann’s position carried the day among other physicists who supported his atomic theories in the debate…His students included …Lise Meitner….On September 5, 1906…Boltzmann hanged himself … tombstone bears the inscription S = k \cdot \log W…Ostwald and many defenders of “pure thermodynamics” were trying hard to refute the kinetic theory of gases and statistical mechanics because of Boltzmann’s assumptions about atoms and molecules and especially statistical interpretation of the second law….This movement around 1900 deeply depressed Boltzmann since it could mean the end of his kinetic theory and statistical interpretation of the second law of thermodynamics….To quote Planck, “The logarithmic connection between entropy and probability was first stated by L. Boltzmann in his kinetic theory of gases”…The second law, [Boltzmann] argued, was thus simply the result of the fact that in a world of mechanically colliding particles disordered states are the most probable.
    Boltzmann’s student, Lise Meitner, “was part of the team that discovered nuclear fission, an achievement for which her colleague Otto Hahn was awarded the Nobel Prize. Meitner is often mentioned as one of the most glaring examples of women’s scientific achievement overlooked by the Nobel committee.”
    – Ray

    • Ray Eston Smith Jr

      By the way, “energy” is much more of an abstraction than “disorder”. The history of the First Law of Thermodynamics (Conservation of Energy) has been the history of scientists inventing new definitions for new forms of energy whenever conservation of energy seemed to fail. However, science did eventually achieve a fundamental understanding of energy, thanks to Emma Noether. Noether’s Theorem says that whenever there’s a symmetry, it implies a conservation law. Conservation of energy can thus be derived from the symmetry of time (i.e. fundamental forces are independent of time, depending only on positions).

      The Second Law (disorder increases) can be derived from the laws of probability. The disorder frequently causes dispersal of energy or matter, but not always. But disorder always increases.

      There is an excellent book, Entropy Demystified by Arieh Ben-Niem which gives a clear, easy-to-understand, common-sense explanation of entropy. Professor Ben-Niem objects to the description “entropy is disorder”. Instead, he says entropy is “lost information.”

  7. Jennifer,

    Thank you so much for the fine summary of my views about the second law and entropy. Since your 2006 comment, the total of chemistry texts that have discarded the unscientific concept of “disorder” has risen to 25, I am happy to report.

    Anyone can inspect the detailed list that starts on the third (print) page of entropysite.oxy.edu. Of course, I am shocked — as Mr. Roy Smith undoubtedly intended! — by his characterizing me: “He is a liar”. And then, he writes “He lists books that he claims he has influenced but, strangely, not a single quote from a single author acknowledging that influence.”

    I hope that Mr. Smith can meet with me sometime at a college campus where, in addition to the texts that I have in my cramped retirement den, I can show him in other professors’ offices the number of texts with such acknowledgments — even though that is not to be expected any more since the deletion of “disorder” has become conventional.

    First, however, for an example I would urge him to check the 4th edition of the best-selling high level gen chem text by Silberberg at a superior college or university near his present residence. On page xviii is “Chapter 20 has been completely rewritten to reflect a new approach to the coverage of entropy. The vague notion of “disorder” (with analogies to macroscopic systems) has been replaced with the idea that entropy is related to the dispersal of a system’s energy and the freedom of motion of its particles.” Then, on p. xix that is headed “Acknowledgments” includes …”Frank Lambert of Occidental College for insightful advice and comments on the coverage of entropy (Chapters 13 and 20)…”

    I do not know Mr. Smith’s background, other than his profound knowledge of Shakespeare and Shakespearean works. But his discourteous and aggressive language is not appropriate nor correct. I do not lie. I do not steal/hijack or con. My life has been straightforwardly devoted to science and science education.

    Although I am not an idiot, neither am I near to a Boltzmann. But Mr. Smith (properly) exalts Boltzmann’s struggles for his revolutionary ideas that changed chemistry and physics from the 1890s on, while he reviles me for mine that have changed concepts in chemistry over the past decade. Mine have been forged by meeting hammer blows by skilled chemists before their publication in scientific journals — and finally their acceptance by textbook authors.

    Mr. Smith has viciously disparaged my referring questioners for information to my central website, entropysite.oxy.edu. I do so because it is as far as imaginable from a glossy website but rather a repository of information and leads to many others’ articles as well as mine, links to other sources of information, supplements — some 35 pages that lead to a total of more than a hundred pages of articles, etc. , re the second law and understanding entropy.

    Thank you, Jennifer, for allowing me this space to respond to Mr. Smith.

    Frank L. Lambert
    Professor Emeritus
    Occidental College
    Los Angeles, CA 90041

  8. Jennifer,

    I just glanced at the foregoing and I apologize to Mr. Smith for mistyping his first name. It should have been Ray.

    Frank L. Lambert

  9. I love the passion and dedication to clarity and truth that I see in these comments.

    In love with the observable phenomena of the universe and humbled by the inability to fully explain it,


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