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?
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.
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.