with which we experiment, if distributed canonically, would therefore appear to human observation as an ensemble of systems in which all have the same energy. We meet with other quantities, in the development of the subject, which, when the number of degrees of freedom is very great, coincide sensibly with the modulus, and with the average index of probability, taken negatively, in a canonical ensemble, and which, therefore, may also be regarded as corresponding to temperature and entropy. The correspondence is however imperfect, when the number of degrees of freedom is not very great, and there is nothing to recommend these quantities except that in definition they may be regarded as more simple than those which have been mentioned. In Chapter XIV, this subject of thermodynamic analogies is discussed somewhat at length. Finally, in Chapter XV, we consider the modification of the preceding results which is necessary when we consider systems composed of a number of entirely similar particles, or, it may be, of a number of particles of several kinds, all of each kind being entirely similar to each other, and when one of the variations to be considered is that of the numbers of the particles of the various kinds which are contained in a system. This supposition would naturally have been introduced earlier, if our object had been simply the expression of the laws of nature. It seemed desirable, however, to separate sharply the purely thermodynamic laws from those special modifications which belong rather to the theoiy of the properties of matter.

Josiah Willard Gibbs (1839–1903) was the greatest American mathematician and physicist of the nineteenth century. He played a key role in the development of vector analysis (his book on this topic is also reissued in this series), but his deepest work was in the development of thermodynamics and statistical physics. This book, Elementary Principles in Statistical Mechanics, first published in 1902, gives his mature vision of these subjects. Mathematicians, physicists and engineers familiar with such things as Gibbs entropy, Gibbs inequality and the Gibbs distribution will find them here discussed in Gibbs' own words.

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The specific blockade of the kainate-induced excitatory conductance is consistent with the ability of TPM to reduce neuronal excitability and could contribute to the anticonvulsant efficacy of this drug.