Abstract
Part II of this three-part paper presents some of the most important theorems that can be deduced from the four postulates of the unified theory discussed in Part I. In Part IIa, it is shown that the maximum energy that can be extracted adiabatically from any system in any state is solely a function of the density operator\(\hat \rho\) associated with the state. Moreover, it is shown that for any state of a system, nonequilibrium, equilibrium or stable equilibrium, a unique propertyS exists which is proportional to the total energy of the system minus the maximum energy that can be extracted adiabatically from the system in combination with a reservoir. For statistically independent systems, propertyS is extensive, it is invariant during all reversible processes, and it increases during all irreversible processes.
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References
G. H. Hardy, J. E. Littlewood, and G. Pólya,Inequalities, Cambridge University Press, London (1967), p. 260.
J. Karamata,Publ. Math. Univ. Belgrade 145(1932); E. F. Beckenbach and R. Bellman,Inequalities, 2nd rev. ed., Springer-Verlag, New York (1965), pp. 30–32.
G. N. Hatsopoulos and J. H. Keenan,Principles of General Thermodynamics, John Wiley and Sons, New York (1965), p. 369.
R. C. Tolman,The Principles of Statistical Mechanics, Oxford University Press, London (1938), pp. 412–414.
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Part I of this paper appeared inFound. Phys. 6(1) (1976). The numbering of the sections, equations, and references in this part of the paper continues from those in Part I.
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Hatsopoulos, G.N., Gyftopoulos, E.P. A unified quantum theory of mechanics and thermodynamics. Part IIa. Available energy. Found Phys 6, 127–141 (1976). https://doi.org/10.1007/BF00708955
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DOI: https://doi.org/10.1007/BF00708955