I read on wikipedia how Clausius came to define entropy after studying the Carnot cycle (He found a relation between heat transfer and temperature which was a state function,and named it entropy) but how this can be related to statistical form of entropy?

  • I believe statistical entropy is more related to the mixing of gases which also infers a volume change by default. Once gases mix energy is lost to entropy, ex: if 2 1 liter vials of pure gas are connected they mix and each now occupies 2L. – PhysicsDave Oct 16 at 12:30
  • This is essentially a duplicate of physics.stackexchange.com/questions/131170/… and many other questions on this site (not all of which have been answered satisfactorily). It is also discussed in any book or course on statistical thermodynamics. The issue, however, is still being discussed, see e.g. RH Swendsen Entropy, 19, 603 (2017). – LonelyProf Oct 16 at 15:54
  • The thermodynamic definition involves temperature, which is less fundamental than entropy. You can therefore simply define entropy in the usual information theoretical way and then define temperature for systems in equilibrium, so that the usual thermodynamical laws are valid. – Count Iblis Oct 16 at 18:31

those two formulations of thermodynamics are developed by the use of completely different initial postulates and reasoning paths. the best exposition I have read on them and how they ultimately lead to the same conclusions is contained in a book by Giedt called Thermophysics.

  • Can you please explain a bit more about that? – user209836 Oct 17 at 2:29
  • the fundamental laws of thermodynamics can be derived in two ways: One by considering bulk properties like temperature, pressure, heat flows and density and one by considering the statistical behavior of a large ensemble of atoms which individually possess mass and kinetic energy. In the end the laws they furnish are identical, but the mathematical pathways to get there are very different. I read Giedt 45 years ago and am not sure it is in print today. – niels nielsen Oct 17 at 5:36
  • ok thanks anyway – user209836 Oct 17 at 7:41

I believe statistical entropy is more related to the mixing of gases which also infers a volume change by default. Once gases mix energy is lost to entropy, ex: if 2 1 liter vials of pure gas are connected they mix and each now occupies 2L.

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