Further Aspects of Thermodynamic Geometry

We also wish to briefly cite other research areas of science, engineering, and mathematics that relate to thermodynamic geometry, but are outside the scope of present discussion. A partial bibliography pertaining to interpretation and applications of thermodynamic geometry is given in Sidebar 13.1. 

The metric geometry of equilibrium thermodynamics provides an unusual prototype in the rich spectrum of possibilities of differential geometry. Just as Einstein s general relativistic theory of gravitation enriched the classical Riemann theory of curved spaces, so does its thermodynamic manifestation suggest further extensions of powerful Riemannian concepts. Theorems and tools of the differential geometer may be sharpened or extended by application to the unique Riemannian features of equilibrium chemical and phase thermodynamics. 

Geometrical tools prove useful in addressing various problems of finite-time thermodynamics and optimal control theory. These methods also have potential applicability to thermodynamic-type applications in subjects ranging from the chemical, biological, and materials sciences to information theory. Efficient vector-algebraic tools allow such applications to be extended to systems of virtually unlimited complexity, beyond realistic reach of classical methods. 

Classical and Geometrical Theory of Chemical and Phase Thermodynamics. By Frank Weinhold Copyright 2009 John Wiley Sons, Inc. 

The rich metric structure of macroscopic thermodynamics also presents unusually stringent tests of theoretical models. Attempts to understand thermodynamic phenomena at a molecular level seem to demand improved dynamical and quantum statistical thermodynamic models that adequately incorporate the subtleties of quantum-mechanical valency and bonding interactions. Development of such models is an active area of modem physical chemistry research, but a more complete survey of the current molecular theory of gases and liquids is beyond the scope of the present work. 

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