Entropy and Information

Abstract

The greatest American scientist of the period between the late nineteenth and early twentieth century was Willard Gibbs (1839–1903). Born in New Haven, Connecticut, he belonged to an old Yankee family that, since the seventeenth century, had produced distinguished clergymen and academics. After earning a Ph.D. at Yale, he traveled through Europe, attending lectures at different qualified Universities. Back home, in 1871, he was appointed chair of Mathematical Physics at Yale, the first such appointment in the United States. His research interest was focused on the extension of thermodynamics to chemical systems in which different phases (gas, liquid, and solid) are present. From such an effort, he wrote a monograph entitled “On the Equilibrium of Heterogeneous Substances”, which begins with a quotation from Rudolf Clausius: “The energy of the world is constant. The entropy of the world tends towards maximum.” Hereafter, Gibbs, rigorously and ingeniously, applied thermodynamics to the interpretation of certain chemical phenomena previously considered a collection of isolated facts and observations. The approach started from the definition of system, chosen as a portion of the Universe, whose behaviour can be characterized by a set of variables. Within this framework, Gibbs became concerned with “their private lives”, which he addressed by setting forth the criteria of “their equilibrium and stability”.