On Time Dependent Entropy vis-a-vis Clausius Inequality: Some of the Aspects Pertaining to the Global and the Local Levels of Thermodynamic Consideration

Abstract

Meixner's revelation in connection with the nonclarity about the
entropy function contained in the differential form of Clausius'
inequality led us to reinvestigate the foundational aspects involved
therein. It is proved that the differential form of Clausius' inequality
contains the entropy function for nonequilibrium states. We have
also augmented the cyclic form of the Clausius' inequality to include
those nonequilibrium situations wherein the system simultaneously
interacts at the different positions of its bounding surface
with the heat reservoirs of different temperatures. It gets once again
established that no local level Clausius' inequality analogue can
ever be devised if the system has a spatial nonunifonnity. Contrary
to Meixner's apprehension one obtains an unique time dependent
entropy function from the cyclic fonn of Clausius' inequality.