Desai and Lieber 



We thus see that the information content of the classical laws of mechanics 

 can be noted in two steps: the first consists of the definition of force equilibrium 

 that characterizes a particular aspect of uniformity, and the second consists of a 

 proposition that is based on the previous definition and which asserts that equi- 

 librium so defined is a condition which is constantly and instantaneously main- 

 tained everywhere in the domain of classical mechanics. Neither in the defini- 

 tion nor in the proposition does the notion of perturbation appear, since all 

 parameters and statements pertaining thereto are brought into correspondence 

 with the instantaneous configuration of a mechanical system. In man's endeavor 

 to grapple with the notion of stability, elucidate its nature, and grasp the phe- 

 nomenon of stability as an aspect of nature, he has endeavored to comprehend it 

 by couching it in definitions. This has produced in the literature many defini- 

 tions of stability, each of which produces different stability criteria. All of these, 

 however, seem to share the notion of a perturbation in terms of which various 

 definitions of stability are formulated. Many of these endeavors inquire into the 

 stability of a mechanical system by subjecting such a system to a perturbation 

 and investigating the subsequent changes the system follows with the passing of 

 time. 



The principle of maximum uniformity identifies the stability of a particular 

 member of a mechanical system with its instantaneous state, and correspond- 

 ingly the global stability of a mechanical system with its instantaneous global 

 state. As in the case of the propositions of classical mechanics, which are ex- '-- 

 pressed in terms of force equilibrium and which assert that this aspect of uni- 

 formity is instantaneously and everywhere constantly maintained in classical 

 mechanical systems, so correspondingly according to the principle of maximum 

 uniformity all realizable states are instantaneously maximum- stable under the 

 instantaneously prevailing forces and the constraints to which the system is in- 

 stantaneously subjected. By this concept of stability there does not exist an 

 instantaneously realizable unstable state, and this concept, like the concept of 

 force equilibrium, does not appeal to the notion of a perturbation, I accordingly 

 believe that Dr. Schmiechen's minimum stability criterion which he derived for 

 the Karman vortex street may be an aspect of the stability principle cited here, 

 and according to which all realizable flows are instantaneously maximum- stable. 



When the principle of minimum dissipation was conceived and originally 

 formulated in hydrodynamical terms as an approximate but reasonable repre- 

 sentation of the restriction on realizable flows implied by the original and re- 

 stricted version of the principle of maximum uniformity, we were cognizant of 

 existing thermodynamical theories of weakly irreversible processes and of the 

 principle of minimum entropy production. We were, however, interested in work- 

 ing within the framework of the description, parameters, and functions that are 

 characteristic of classical hydrodynamics, and therefore were interested in 

 formulating restrictions on realizable flows in terms of these, such as, for ex- 

 ample, the dissipation function. Furthermore, by so doing we do not necessarily 

 restrict the conditions of realization of actual flows which were introduced to 

 augment the Navier- Stokes equations, to weakly reversible processes. In this 

 regard it is interesting to note that Prigogine, who, I believe, established the 

 principle of minimum entropy production as a theorem in 1947 for highly re- 

 stricted conditions, has only recently considered and used the principle of 



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