Leipzig: Barth, 1903. 1st Edition. JOURNAL ISSUE, ORIGINAL WRAPPERS. 1st EDITION OF EINSTEIN’S DERIVATION OF ENTROPY FROM THERMODYNAMIC PRINCIPLES. “Einstein showed that the concepts of temperature and entropy follow from the assumption of the energy principle and atomic theory. He required only the foundations of atomic physics but no other physical hypotheses” (Calaprice, The Einstein, Almanac, 4). Weil No. 4. Boni 4. [We also offer the bound volume separately].
In a series of three papers published between 1902 and 1904, Einstein explores “the derivation of the properties of thermal equilibrium on the basis of the mechanical equations of motion and of the calculus of probabilities,… [focusing specifically] on fluctuations of the energy as a possible tool for establishing the validity of this foundation” (Peliti & Rechtman, Einstein’s Approach to Statistical Mechanics).
In his 1902 paper, Einstein writes “in his introduction that nobody has yet succeeded in deriving the conditions of thermal equilibrium and of the second law of thermodynamics from probability considerations, although Maxwell and Boltzmann came near to it. Willard Gibbs is not mentioned. In fact, Einstein's paper was written in ignorance of Gibbs paper published 1901. In the present paper, Einstein builds the theory on another basis not used by Gibbs, namely on the consideration of a single system in course of time (later called "Zeit-Gesamtheit", time assembly), and proves that this is equivalent to a certain virtual assembly of many systems, Gibb's micro-canonical assembly. Einstein at once proceeded to apply his theorems to a case of utmost importance, namely to systems of a size suited for demonstrating the reality of molecules and the correctness of the kinetic theory of matter."(Walter Alicke).
In the paper offered, the second of the three and entitled in English “A Theory of the Foundations of Thermodynamics,” “Einstein asks whether kinetic theory is essential for the derivation of the postulates of thermal equilibrium and of the entropy concept, or whether “assumptions of a more general nature” could be sufficient” (ibid). In other words, Einstein, as noted earlier, wanted to know if thermodynamic laws could be obtained using a minimum amount of elementary assumptions.
And Einstein was able to do just that, to derive entropy in such a way that it did not require any particular set of time evolution equations to remain valid; to “connect the entropy of a system at thermal equilibrium with the corresponding phase space quantities” (Norton, Einstein’s Miraculous Argument of 1905). He argues: “It is sufficient that such a set of equations respects a more general property, namely that a suitably defined ‘incompressibility’, in the phase space of an aggregate of molecules, be preserved in the time evolution. The usual decomposition of energy into kinetic and potential is not required, either” (Navarro, Gibbs, Einstein and the Foundations of Statistical Mechanics). “In the closing section of this paper Einstein applies these results to a simple description of a thermal engine connected in turn to several heat reservoirs to derive the second principle in the form of Clausius” (Peliti & Rechtman). Item #1361
CONDITION & DETAILS: Leipzig: Barth. 1903. 4to. (9 x 6 inches; 225 x 150mm). Issue in original wrappers in very good condition, housed in a custom pamphlet case, gilt-lettered at the spine.