There are nice thermodynamical definitions of spontaneous processes and reactions: entropy increase, or negative Gibbs free energy for constant pressure and temperature.
Are there equally nice and straightforward characterizations of the spontaneity of quantumphysical processes, radioactive decay, spectral radiation, etc. - to which I would also like to reckon qm measurement, possibly in order to diminish its “mysteries”.
In particular, can van Neumann entropy used to define spontaneity for quantumphysical processes? The answer would seem: No. Certainly, the analogy with thermodynamical entropy is poor (despite von Neumann’s concocted thought experiment).
If not, then, are there other ways to characterize spontaneous qm processes?
It is my belief that indeed radioactive decays are entropy increasing phenomena. However proving this statement is not easy. Nevertheless, they occur spontaneously, therefore they are for sure entropy non-decreasing phenomena. But whether entropy is actually increasing (and hence the radioactive decay process is irreversible) requires proof, which I do not have (yet).
Thermodynamic entropy and Gibbs free energy criterion can be used to define spontaneity for quantum physical processes, if the answer is no, the second law will be not valid.
it is similar to chemical thermodynamics, the entropy production diS>=0, or Gibbs free energy criterion dG=0, where T is the temperature of the energy conversion, using diG denote Gibbs free energy production, we have diG=-diq
dear Tang Suye, thanks a lot for your answer
Only: HOW to define the standard Gibbs free energy of formation of an element for quantum physical processes?
Formation out of protons, neutrons, electrons? Or out of quarks, etc?
Many suggest to use von Neumann entropy
But that is (also an analogy and) a different story, or isn’t it?
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