Myths and Verities in Protein Folding Theories, World Scientific.
Contributions to statistical mechanics in terms of information theory
In 2017, Ben-Naim posted three articles in arXiv. In those articles, three radical ideas were introduced into a field which is considered as classical. The ideas followed from the new definition of entropy based on Shannon's measure of information. The three ideas are, briefly, as follows. First, there is no relationship between either entropy or the second law of thermodynamics and the so called arrow of time. This false association between the Second Law and time was first suggested by Arthur Eddington. Also the Boltzmann's H-Theorem is not about the time dependence of the entropy, but the time dependence of the Shannon's measure of information. In this respect Boltzmann erred in interpreting his H function as entropy. Second, the application of the concept of entropy to the entire universe is unwarranted. This association has its origin in Clausius' statement that the entropy of the World always increases. Clausius, who is credited for the formulation of the second law, did not and could not understand the molecular interpretation of entropy. Unfortunately, the application of the concept of entropy to the entire universe features in many textbooks and in popular science books. This erroneous application is discussed in great detail in Ben-Naim's recent books: The Briefest History of Time, Entropy, the Truth the whole Truth and nothing but the Truth, and in Information, Entropy, Life and the Universe. Third, the application of entropy and the Second Law to living organisms is totally unwarranted. The most famous statement about entropy and life was made by Erwin Schrödinger, in his book What is Life?. In this book, Schrödinger not only discusses entropy and life and associates entropy with disorder, he also "invents" the concept of "negative entropy," which was later renamed negentropy by Léon Brillouin. This erroneous application is further discussed in Ben-Naim's books. Ben-Naim is a modern antagonist of the term entropy. He advocates abandoning the word entropy altogether, and replacing it with "missing information". He also indicates that the Kelvin temperature scale artificially introduces the units of thermodynamic entropy. Because this temperature scale was introduced before the atomic, microscopic nature of matter was widely accepted, the Boltzmann constant was necessary. S = kBlog could be expressed simply as S = log, if the energy units for temperature kBT were used. An example of the insight that information theory can bring to statistical mechanics is the rederivation of the Sackur-Tetrode equation. It results from stacking the missing information due to four terms: positional uncertainty, momenta uncertainty, quantum mechanical uncertainty principle and the indistinguishability of the particles. Books written by Arieh Ben-Naim on entropy and statistical mechanics include:
