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Entropy Demystified: The Second Law Reduced To Plain Common Sense (Revised Edition)
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Product details
Paperback: 262 pages
Publisher: World Scientific; Expanded ed. edition (June 18, 2008)
Language: English
ISBN-10: 9812832254
ISBN-13: 978-9812832252
Product Dimensions:
6 x 0.6 x 9 inches
Shipping Weight: 1 pounds (View shipping rates and policies)
Average Customer Review:
4.2 out of 5 stars
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Amazon Best Sellers Rank:
#442,807 in Books (See Top 100 in Books)
Arieh Ben-Naim, professor at the Hebrew University of Jerusalem, taughtthermodynamics and statistical mechanics for many years and is wellaware that students learn the second law but do not understand it,simply because it can not be explained in the framework of classicalthermodynamics, in which it was first formulated by Lord Kelvin (i.e.William Thomson, 1824-1907) and Rudolf Julius Emanuel Clausius(1822-1888). Hence, this law and the connected concept of entropy areusually surrounded by some mysterious halo: there is something (theentropy), defined as the ratio between heat and temperature, that isalways increasing. The students not only do not understand _why_ it isalways increasing (it is left as a principle in classicalthermodynamics), but also ask themselves what is the _source_ of suchever increasing quantity.We feel comfortable with the first law, that is the principle of energy conservation, because our experience alwayssuggests that if we use some resource (the energy) to perform any work,then we are left with less available energy for further tasks. Thefirst law simply tells us that the heat isanother form of energy so that nothing is actually lost, something whichwe can accept without pain. In addition, the second law says that,though the total energy is constant, we can not always recycle 100% ofit because there is a limit on the efficiency of conversion of heat intowork (the highest efficiency being given by the Carnot cycle, namedafter Nicolas Léonard Sadi Carnot, 1796-1832). Again, we can accept itquite easily, because it sounds natural, i.e. in accordance with ourcommon sense: we do not know any perpetual engine. But our dailyexperience is not sufficient to make us understand what entropy is, andwhy it must always increase.The author shows that, if we identify the entropy with the concept of"missing information" of the system at equilibrium, following the workdone by Claude Elwood Shannon (1916-2001) in 1948, we obtain a welldefined and (at least in principle) measurable quantity. This quantity,apart from a multiplicative constant, has the same behavior as theentropy: for every spontaneous process of an isolated system, it mustincrease until the equilibrium state is reached. The missinginformation, rather than the disorder (not being a well definedquantity), is the key concept to understand the second law.I should say here that the identity of entropy and missinginformation is not a widespread idea among physicists, so that manypeople may not appreciate this point. However, the arguments of thisbook are quite convincing, and different opinions are also taken intoaccount and commented.In addition, Ben-Naim thinks that the entropy should be taught as andimensionless quantity, being defined as the ratio between heat, that isenergy, and temperature, that is a measure of the average kinetic energyof the atoms and molecules. The only difference with the missinginformation, again dimensionless, is the scale: because the missinginformation can be defined as the number of binary questions (withanswer "yes" on "no" only) which are necessary to identify themicroscopic state of the system, this number comes out to be incrediblylarge for ordinary physical systems, involving a number of constituentsof the order of the Avogadro's number. This numerical difference makesme think about the difference between mass and energy, connected by theEinstein's most famous equation E = m c^2: they could be measured usingthe same units (as it is actually done in high-energy physics), the soledifference being that even a very small mass amounts to a huge quantityof energy.The mystery of the ever increasing entropy can be explained once (andonly if) we realize that the matter is not continue, but discrete. Theauthor basically follows the work of Josiah Willard Gibbs (1839-1903),who developed the statistical mechanical theory of matter based on apurely probabilistic approach. First, one has to accept the fact thatmacroscopic measurements are not sensitive enough to distinguishmicroscopic configurations when they differ for thousands or evenmillions of atoms, just because the total number of particles is usuallyvery large (usually of the order of 10^23 at least). Then, under thehypothesis that each microscopic state is equally probable, i.e. thatthe system will spend almost the same time in each micro-state, one cangroup indistinguishable micro-states into macro-states. The latter arethe only thing we can monitor with macroscopic measurements. Under thecommonly accepted hypothesis that all microscopic configurations areequally probable, macro-states composed by larger numbers ofmicro-states will be more probable, i.e. the system will spend more timein such macro-states.As a naive example, one could start with a system prepared in such a waythat all its constituents are in the same microscopic configuration.One could think about a sample of N dices, all of them showing the sameface, say the first one. The questions could be: (1) "Are all dicesshowing the same face?"--Yes--; (2) "Is the face value larger or equalthan 3?"--No--; (3) "Is the face value larger or equal than 2?"--No--;at this point we know that the value is 1. In general, the number ofbinary questions is proportional to the logarithm in base 2 of thenumber C of possible configurations, that is O(log_2 C). Now imagine torandomly mix the dice by throwing all of them. The answer to the firstquestion would be "No", so that a completely different series ofquestions has to be asked to find the microscopic configurations.First, one may procede by finding how many dice show the value 1, forexample, asking O(log_2 N) questions. Suppose that the answer is MAdam Smith's "Invisible Hand" leads many people to think, that markets have the power to repair "themselves". But even in markets as open systems, there are irreversible processes, as the openness of real systems always is limited. Adam Smith, still in a Newtonian world, didn't know anything about the "second 'law' of thermodynamics" and "entropy". But at least today we should know better. Unfortunately entropy still seems to be some mystic thing to many, which to deal with should be avoided. (Knowing about entropy also increases responsibility. Some like to avoid that as well.)You can't "avoid" entropy. Entropy is something very real: E.g. in broadband transmission the cost (e.g. chip size, power dissipation, heat generation) of managing entropy is almost proportional to the amount of entropy, which is to be managed. And climate change also can be explained by the entropy accounting (entropy generation, import, export) of the biosphere and the clogging of the interfaces of the biosphere, which are required to get rid of the entropy generated within the biosphere.Therefore we need comprehensible explanations for entropy. My personal interest is not so much in entropy itself, but in how teachers and authors manage to explain entropy. Arieh Ben-Naim manages to get rid of all the fuzz which comes with so many publications related to entropy. He really manages to demystify entropy. I think, there are two paths which one could select to explain entropy. One is within information theory, the other one uses statistical physics. Ben-Naim chose the second one and thus not only managed to demystify entropy, but also demystified statistical physics: From my point of view, you just need a high school degree in order to be able to comprehend his book. Or you even may be lucky to have a teacher, who uses this book in the final high school year.Economists and social scientists could get some help from the book too in understanding, what entropy really means. Indicators like the inequality measures of Theil and Kolm are entropy measures. And Nicholas Georgescu Roegen will be easier to understand. (The book would have been helpful to him too.)Besides its content, I also like the making of the little book from Arieh Ben-Naim. It got very nice illustrations. And they are not just nice, they also are helpful. Here scientific thinking comes together with simple love to make things beautiful. It seems, that good science also leads to good aesthetics.Related to this book, I also recommend the publications of M.V.Volkenstein (like Physics and Biology), although they are mostly out of print.
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!
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