In a previous paper (Duncan, T.L., Semura, J.S. in Entropy 6:21, 2004) we considered the question, “What underlying property of nature is responsible for the second law?” A simple answer can be stated in terms of information: The fundamental loss of information gives rise to the second law. This line of thinking highlights the existence of two independent but coupled sets of laws: Information dynamics and energy dynamics. The distinction helps shed light on certain foundational questions in statistical mechanics. For (...) example, the confusion surrounding previous “derivations” of the second law from energy dynamics can be resolved by noting that such derivations incorporate one or more assumptions that correspond to the loss of information. In this paper we further develop and explore the perspective in which the second law is fundamentally a law of information dynamics. (shrink)

The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be defined unambiguously, but it is the time derivative or entropy production that governs ongoing processes in these systems. The differences in physical interpretation and thermodynamic role of entropy in equilibrium and nonequilibrium systems is emphasized and the observable aspects of entropy production are (...) noted. A basis for nonequilibrium thermodynamics is also outlined. (shrink)

In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, _Godel’s Proof_ by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy (...) the chance to satisfy their intellectual curiosity. (shrink)

First English translation of revolutionary paper that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.

The results of two recent articles expanding the Gibbs variational principle to encompass all of statistical mechanics, in which the role of external sources is made explicit, are utilized to further explicate the theory. Representative applications to nonequilibrium thermodynamics and hydrodynamics are presented, describing several fundamental processes, including hydrodynamic fluctuations. A coherent description of macroscopic relaxation dynamics is provided, along with an exemplary demonstration of the approach to equilibrium in a simple fluid.