A Rigorous Development of the Second Law

Statistical mechanics attributes the origin of the second law to the molecular nature of matter (see Sections 3.13 and 16.5.2, and for a detailed discussion Denbigh, 1981, p.56). It also provides a quantitative relationship between entropy and molecular behavior through a comparison of statistical analogies with thermodynamic functions (this is eloquently done 

In support of the second postulate we have the fact that whenever the Schrodinger equation can be solved (the ideal gas for example), the results agree with the experimental observations. This, of course, is the same type of support given to the second law. 

Have we, thus, indeed a rigorous development of the second law Are we closer to the ultimate truth Or, have we just fallen victims of the famous slogan of theoretical mathematicians Die road to complete rigor leads to meaninglessness  

We have associated knowledge of molecular behavior with the second law in Sections 3.13 and 16.5. Let us now compare the ideas about this knowledge from the classical and quantum mechanics points of view. 

For the first, here is what the famous French mathematician Pierre Laplace, who set out to refine and perfect Newton s calculations, writes 

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