Re: Why does entropy have to increase? (advanced answer)

I learned about statistical mechanics as an undergrad, but the reason why
entropy should always increase seemed like a postulate to me.
It is a postulate. Unlike the rest of statistical mechanics, it can't be
derived from the underlying physical laws (the standard model)
Statistical mechanics is a theory of arbitrary system with energies and does
not consider particle physics in its basic concepts. If you now want to
apply statmech to say a gas of atoms, then the conditions of applicability
have to be clearly set.

If I knew the underlying concept why {\sum p_i \ln p_i} is supposed to be a
maximum, I would understand better when statmech is appropriate to a
system.

Postulates are fine, but if you "apply" them to a specific case such as the
motion of gas atoms, a problem which is mechanically complete defined even
without entropy, then you have to justify that.

I believe there are theories mentioning words like Markov processes and
ergodicity, but I haven't found a source where I can read up the
justification of entropy. Anyone aware of these?

So basically statmech is a purely mathematical theory of weakly interacting
systems, and it's important to know which physical problem these model
apply to.

Anton
.

Relevant Pages

  • Re: Is evolution an example of decreasing entropy?
    ... >> The Entropy of Thermodynamics is a physical concept, ... >> the entropy of statistical mechanics when the probability distribution ... So the individual quantum states ... >> The Entropy of Statistical Mechanics obeys the Second Law ...
    (talk.origins)
  • Re: Why does entropy have to increase? (advanced answer)
    ... entropy should always increase seemed like a postulate to me. ... microstates, and further, that the measures of microstates -- so-called ... entropy increases either going forward or backward in the Markov chain: ...
    (sci.physics)
  • Re: Is evolution an example of decreasing entropy?
    ... >> Statistical entropy and thermodynamic entropy are one and the same. ... The Entropy of Statistics is a mathematical concept. ... The Entropy of Thermodynamics is a physical concept, ... the entropy of statistical mechanics when the probability distribution ...
    (talk.origins)
  • Re: Is evolution an example of decreasing entropy?
    ... >>> Statistical entropy and thermodynamic entropy are one and the same. ... > The Entropy of Statistics is a mathematical concept. ... > The Entropy of Thermodynamics is a physical concept, ... > the entropy of statistical mechanics when the probability distribution ...
    (talk.origins)
  • Re: Is evolution an example of decreasing entropy?
    ... >>> Statistical entropy and thermodynamic entropy are one and the same. ... > The Entropy of Statistics is a mathematical concept. ... > The Entropy of Thermodynamics is a physical concept, ... > the entropy of statistical mechanics when the probability distribution ...
    (talk.origins)
Quantcast