Equilibrium relationships for non-equilibrium chemical dependencies

In contrast to common opinion, it is shown that equilibrium constants determine the time-dependent behavior of particular ratios of concentrations for any system of reversible first-order reactions. Indeed, some special ratios actually coincide with the equilibrium constant at any moment in time. This is established for batch reactors, and similar relations hold for steady-state plug-flow reactors, replacing astronomic time by residence time. Such relationships can be termed time invariants of chemical kinetics

Reflective Equilibrium

This article examines the method of reflective equilibrium (RE) and its role in philosophical inquiry. It begins with an overview of RE before discussing some of the subtleties involved in its interpretation, including challenges to the standard assumption that RE is a form of coherentism. It then evaluates some of the main objections to RE, in particular, the criticism that this method generates unreasonable beliefs. It concludes by considering how RE relates to recent debates about the role of intuitions in philosophy

Perfect Regular Equilibrium

We propose a revised version of the perfect Bayesian equilibrium in general multi-period games with observed actions. In finite games, perfect Bayesian equilibria are weakly consistent and subgame perfect Nash equilibria. In general games that allow a continuum of types and strategies, however, perfect Bayesian equilibria might not satisfy these criteria of rational solution concepts. To solve this problem, we revise the definition of the perfect Bayesian equilibrium by replacing Bayes' rule with a regular conditional probability. We call this revised solution concept a perfect regular equilibrium. Perfect regular equilibria are always weakly consistent and subgame perfect Nash equilibria in general games. In addition, perfect regular equilibria are equivalent to simplified perfect Bayesian equilibria in finite games. Therefore, the perfect regular equilibrium is an extended and simple version of the perfect Bayesian equilibrium in general multi-period games with observed actions

The hydrostatic equilibrium and Tsallis equilibrium for self-gravitating systems

Self-gravitating systems are generally thought to behavior non-extensively due to the long-range nature of gravitational forces. We obtain a relation between the nonextensive parameter q of Tsallis statistics, the temperature gradient and the gravitational potential based on the equation of hydrostatic equilibrium of self-gravitating systems. It is suggested that the nonextensive parameter in Tsallis statistics has a clear physical meaning with regard to the non-isothermal nature of the systems with long-range interactions and Tsallis equilibrium distribution for the self-gravitating systems describes the property of hydrostatic equilibrium of the systems.Comment: 7 pages, 9 Reference

Equilibrium Statistical Mechanics

An introductory review of Classical Statistical MechanicsComment: 56 page