Entropy Demystified: The Second Law Reduced To Plain Common Sense (Revised Edition) by Arieh Ben-Naim (PDF)

Description

In this unique book, the reader is invited to experience the joy of appreciating something which has eluded understanding for many years – entropy and the Second Law of Thermodynamics. The book has a two-pronged message: first, that the second law is not infinitely incomprehensible as commonly stated in most textbooks on thermodynamics, but can, in fact, be comprehended through sheer common sense; and second, that entropy is not a mysterious quantity that has resisted understanding but a simple, familiar and easily comprehensible concept. Written in an accessible style, the book guides the reader through an abundance of dice games and examples from everyday life. The author paves the way for readers to discover for themselves what entropy is, how it changes, and, most importantly, why it always changes in one direction in a spontaneous process. In this new edition, seven simulated games are included so that the reader can actually experiment with the games described in the book. These simulated games are meant to enhance the readers’ understanding and sense of joy upon discovering the Second Law of Thermodynamics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Fifty years ago, Arieh Ben-Naim, as every student in a physics or chemistry class of that era, was mystified by his introduction to entropy and the second law of thermodynamics. Although he was a professor of chemistry before retiring 15 years ago, Ben-Naim has evidently not kept up with the teaching of those topics in current chemistry texts. Thus, he seems unaware that most general chemistry texts currently published in the US (16) and three in physical chemistry – most available from Amazon.com – now clearly and simply present entropy and the second law. Therefore, his 217 pages of “Entropy Demystified” that are necessary to develop his personal viewpoint (an information theory variant, not present in a US undergraduate chemistry textbook) can be clarified by 3-4 pages in any of the chemistry texts listed with their ISBN numbers (for exact Amazon.com identification) in […] at “May 2009”. In fact, a conceptual summary of the second law and entropy for most interested readers can be abstracted from these texts in two sentences: “Energy of all types changes from being localized to become more dispersed, spread out, distributed in space (and abstractly, in more energy quantum states, microstates) if that energy is not constrained.” Then, “entropy change is the quantitative measure of how much more widely distributed the initial energy becomes in a spontaneous process.” Thus, in real processes, energy spreads out spatially. Probabilistic methods are one way of quantifying thermodynamic entropy. Unfortunately, Professor Ben-Naim’s fundamental error, summarized on page 204 but weakening all previous pages, is his misinterpretation of what occurs in real systems of molecules, especially in the simple isothermal expansion of ideal gases or in their “mixing”/expansion. These cases have misled him to focus on their particular lack of change in the total energy of the system, rather than on what is the fundamental cause of all thermodynamic entropy change: the increased spreading of the initial energy of actual molecules in space when constraints are removed – e.g., their spontaneously moving into a greater volume from a smaller volume (with unchanged energy) in a process such as expansion/mixing. This is what traditional thermodynamic entropy readily measures and, as just stated, can be readily understood. The disconnect between information and the second law is stressed on page 203 by “a measure of information cannot be used to explain the Second Law of Thermodynamics.” This is true, indeed. The connection between the second law and information is tenuous. Contrast this with the modern view in beginning collegiate chemistry texts, e.g. “whenever a product-favored chemical or physical process occurs, energy becomes more dispersed…This is summarized in the second law of thermodynamics, which states that the total entropy of the universe … is continually increasing.” (Moore, Stanitski, and Jurs; 3rd edition.) A physical chemistry text that is used world-wide states “…the Second Law of thermodynamics, may also be expressed in terms of another state function, the entropy, S. …entropy…is a measure of the energy dispersed in a process…” (Atkins and de Paula, 8th edition.) The connection between spontaneous chemical reactions or physical processes, dispersal of energy, and entropy is integral, tight, and generally accepted. It does not require 200 pages to justify.

⭐I consider this book to be of great value to be read by any scientist (I am one, hence I will not speak for non-scientists).Anyone who learns entropy in terms of thermodynamics (that is, heat cycles) is done a horrible disservice. The microscopic view of entropy makes intuitive sense, and most people do get it. I, however, was stuck for the longest time in that I could not understand why the thermodynamic definitions of entropy were intuitively obvious, why they had to exist, from purely macroscopic reasoning. Ben-Naim clarifies, as most professors of this subject do not or probably do not know, that it is not possible to justify such equations based purely on reasoning.Additionally, Ben-Naim describes entropy itself in terms of information theory. This is invaluable; it is far more rigorous than the naive “disorder” analogy. Anyone who has done more than just basic qualitative questions recognizes that the notion of “ordered” vs “disordered” is inherently fuzzy in examples of solvation. The value of using information theory to then discuss tempergy, or temperature in units of energy, is intuitively valuable.Ben-Naim also discusses entropy as a generalized property from several different common views, which are equivalent. The argument of showing how a certain quantity, seemingly different because of the dependent variable, is actually logically the same is an argument familiar to physicists, helping to put the macroscopic notion of entropy put on firm footing, and not the “Where did this come from” basis of saying it is the contour integral of the change in heat per temperature.If you are a scientist, you will fly through this book, and reap quick rewards. Chemists/Physicists will be already quite used to much of the material in the book, but the analysis of certain chapters (for me, 2, 6, and his epilogue 8) are invaluable, clearly spoken insights.He also offers to send him an email if you are confused!This is what science should be: writing done without pretension (in contrast to Atkins).

⭐I join the chorus of voices praising this book. Finally we have a solid explanation of the concept of entropy as a direct term comind out of probability theory (and indeed from elementary combinatorics). I have long understood that there is some relationship between entropy and probability theory, having been told that systems move from state A to state B because “there are more ways of being in state B than in state A,” but never before has the notion of a “state” been explained to me with even the slightest precision–in particular, I’ve wondered how different states are to be distinguished from one another if not by the arbitrary choice of whoever’s asking the question. Dr. Ben-Naim provides that explanation, and, although there now seems to me that there is indeed some dependence on the particular question being asked, the nature of that dependence is also explained. Not only does Dr. Ben-Naim explain what it means for there to be more ways of being in state B than in state A, he demonstrates how to count the ways!I would have liked a more detailed illustration of games where there are more than two possibilities (for example, left and right or heads or tails) for the appearance of each fundamental particle or coin–for example, I wonder what the appropriate dim states for a system in which there are a decent number (say at least 10) balls, each of which is to be placed in one of at least 3 boxes–but I suspect that the number of readers who might want to see that is small, and it’s a lot of work (at least enough that I don’t expect to explore it).Great book!

⭐As a way of explaining the second law of thermodynamics and especially the elusive and mysterious concept of entropy this is a fascinating book. It attempts to introduce this concept without the use of physical concepts, or at least states this as its aim. It states that noone needs any knowledge of maths or physics to follow the account. However, this is not actually true since throughout the author refers, at many stages, to physical concepts with little explanation. It must also be stressed that he attempts to explain entropy through the use of probability in it most basic foundation. Remarkably, he succeeds and explains some of the central aspects of thermodynamics such as equilibrium without recourse to any physics at all merely through the basic laws of probability. This gives the strong impression that thermodynamics is actually simply mathematics and no physics is required at all. Then in one of the last chapters he attempts to connect his earlier probabilistic explanations with physical reality through the usual gas molecules partitioned between two volumes, the left full of gas and the right empty of gas, when the partition is released. It then comes unstuck to some degree since he very quickly makes this connection without it being at all convincing. For example: the probability of any molecule crossing the distance from one side of the volume across the barrier (which remains open enough for one molecule to cross and for a very short time) is the same for each of the molecules on the left hand side. This seems totally unbelievable since only molecules near the partition can hope to cross it in the time available and then only if their velocity vectors are oriented towards the right. Now I am not saying he is wrong but merely that he gives the impression that this unbelievable thing is the case, instead he should have stated maybe that the probability of any molecule, where you do not know where each is located, is the same.For the most part, the book is an excellent demonstration of what probability can achieve and also how simple such demonstrations can be as well as how convincing these demonstrations can be. It is in the remains of the book where he attempts the connections to physical reality that it falls down.

⭐A thought-provoking book suitable for non-specialists. It briefly describes the conventional formulations of the law before providing detailed illustrations of how changes are ‘driven’ in terms of probability, and of entropy’s description of these changes in terms of ‘missing information’. Perhaps the middle section has a few too many extra illustrations, but, overall, the book is engaging and leaves the reader with a solid understanding of change in simple systems.

⭐In this easy-to-read book, the author explains the nature of entropy using vary basic probabilistic arguments. The author assumes that the reader knows no mathematics, nor has any knowledge of physics but can use ordinary common sense in reasoning things out. Most of the arguments make use of dice and coins until near the end where real systems, e.g., gasses, are discussed. The writing style is very clear, authoritative, highly accessible and friendly. Some concepts and conclusions are deliberately repeated; this can be quite useful to readers who are new to this subject. The book’s level is very basic and could be easily understood by any interested general reader or high school student.

⭐I’m currently in 9th grade and resarching entropy for my monograph. This book was very helpful, explaining concepts I often mystified, in a rather ellegant fashion. I highly reccomend it to anyone looking for a better understanding of the topic, because this book was the one that assisted me the most towards understanding entropy 🙂 thanks Arieh, 5/5

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