Re: [Fis] Re: quantum entropy

   Folks,

   Sergey Trigger and Thorsten Poeschel made a good point as referring to
the relationship between the quantum entropy or the von Neumann entropy and
the Wigner function. Of course, there should be a long way to go to reach
standard thermodynamic entropy as starting from the von Neumann entropy.
Even worse, we are not sure at this moment whether this would be a promising
enterprise likely to succeed, though there have been a few toy models for
its favor. Quantum mechanics is notorious in making the phase-space
probability distribution or density function, i.e., the Wigner function, not
necessarily positive-definite. Nonetheless, the participation of the density
function will be inevitable if the process of measurement is seriously taken
in quantum mechanics. At this point may enter Pedro's biological
contamination.

   In order to calculate either the von Neumann entropy or the Wigner
function, we would definitely require to answer the question of what is the
basis set to rely upon or the unit to count on. The basis set is defined as
the set each member of which is taken not to decohere any further on its
own. The real question is what would the basis set look like. As far as
non-biological realm is concerned, physicists have earned a good reputation
in zeroing in the right basis set. However, material processes can proceed
without the supervision by the overseeing physicists. Biology is just a case
in point. One requirement for serving as the basis set is its robustness
against the environmental disturbances or decoherences. What is most
intriguing is that biological stuff is extremely sophisticated in contriving
robust quantum phenomena for their own sake far beyond our mere theoretical
imagination. If we are lucky enough to identify any part of the robustness
of quantum phenomena in nature, it would certainly help us in picking up the
right basis set in physics in general.

   Cheers,
   Koichiro

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Received on Tue May 11 05:22:10 2004