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Statistical Physics: A Probabilistic Approach

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Whether one likes or dislikes the approach of this book, agrees or disagrees with some of the more controversial results, no-one who has read it can deny that it is a significant book in the field of statistical thermodynamics. Although there are several truly excellent texts on this important subject readily available, this one is refreshingly different,- genuinely making use of established results in mathematical statistics to tackle problems in physics! The method of maximum likelihood and limit theorems such as the central limit theorem and the law of large numbers are examples of results used here which are well-known to, and widely used by, statisticians but generally unfamiliar to many in the field of statistical physics. However, as claimed in the preface, this book's unifying theme is the connection between entropy and probability via a law of error which has caused some consternation in the past but, although an early reference is in a work by Gauss, the result is readily accessible in Keynes' book "A Treatise on Probability". The author also obviously believes passionately that it is wrong to consider physical theories separately from the historical contexts in which they were concerved. Including this historical information when considering such topics as the link between entropy and probability or the case of black body radiation, to mention two examples, provides extra fascinating material which helps make the subject more alive. The approach adopted throughout is, as already stated, different from that normally used and it is, therefore, possibly not surprising that some different and indeed controversial results should emerge: - the phenomenon of Bose-Einstein condensation is examined from a new viewpoint and a transition temperature of 1.98K is derived; phase transitions are examined afresh, although here the claim that phase transitions of higher than second order do not exist surely needs to be re-examined; recent claims for the existence of a fifth ensemble are shown to be in error; and probably most controversial of all is the examination of the generally accepted expression for the entropy of a black hole which shows that the said expression leads to violation of the Second Law of Thermodynamics. However, in the final analysis, this is not a book to be left on a prominent coffee table but rather one to be read! On reading it, some will be angry, some thrilled, but all will be forced to think! Surely that is the mark of a good book.