preprints.org > physical sciences > fluids and plasmas physics > doi: 10.20944/preprints201811.0438.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 16 November 2018 / Approved: 19 November 2018 / Online: 19 November 2018 (09:42:08 CET)

This is a review of efforts to discover action principles for Hydrodynamics and Thermodynamics. The work began with a determined attempt to create sources for Einstein's equations that describe continuous matter - as opposed to point particles. This requires a relativistic action principle. This report is mainly about (non relativistic) Adiabatic Thermodynamics, non equilibrium thermodynamics based on the method of Gibbs. The main relations of classical thermodynamics can be derived from an action principle, in the classical global form and in the local form advocated by Callen. The entropy is defined as the negative derivative of the free energy (free energy density) with respect to the volume (density). This is integrated with an action principle for hydrodynamics that was known to Lagrange in 1760. It is strongly limited to irrotational velocity fields, nevertheless it provides the needed Lagrangian for a large part of thermodynamics. This is the subject of the first 3 sections. It includes a brief review of a new theory of mixtures. The most difficult part of the program has been the discovery of Conservative Hydrodynamics with the required four independent degrees of freedom, with general flows. We give an account of the genesis and the structure of this theory, then a tour of recent applications.

entropy; thermodynamics; conservative hydrodynamics; rotations; meniscus; planets; negative pressure

Physical Sciences, Fluids and Plasmas Physics

* All users must log in before leaving a comment