Leipzig: Barth, 1913. 1st Edition. FIRST EDITION IN ORIGINAL WRAPPERS OF ROSENTHAL’S IMPORTANT PROOF THAT THAT THE ERGODIC HYPOTHESIS IS INCORRECT FOR ANY MECHANICAL SYSTEM. In 1913, German mathematician Artur Rosenthal (1887–1959) set out to answer the question “Can a mechanical system eventually pass through ever point on the energy surface in its phase space? Provoked little more than politely-stifled yawns from phsicists, but introduced a major new branch of mathematical research (Brush, Milestones in Mathematical Results, Transport Theory and Statistical Physics, 1, 1971). His work (along with Plancheral’s) “closed the first phase of a discussion of the foundations of statistical mechanics in which Maxwell, Boltzmann, and Ehrenfest were major participants” (ibid).
Ergodic theory is a branch of mathematics examining dynamical systems with an invariant measure and related problems, its development was motivated by problems of statistical physics. It developed as something of an offshoot from the work on the kinetic theory of gases of Boltzman and Maxwell. “The strategy underlying ergodic theory is to focus on simple yet relevant models to obtain deeper insights about notions that are pertinent to the foundations of statistical mechanics while avoiding unnecessary technical complications.
Ergodic theory abstracts away from dynamical associations including forces, potential and kinetic energies, and the like… It focuses on certain structural and dynamical features that are deemed essential to understanding the nature of the seemingly random behaviour of deterministically evolving physical systems. The selected features were carefully integrated, and the end result is a mathematical construct that has proven to be very effective in revealing deep insights that would otherwise have gone unnoticed” (Stanford Encyclopedia of Philosophy). Item #1524
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