# Can anyone explain equivalence of statistical entropy and thermodynamic entropy?

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 '18 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 '18 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 '18 at 18:31