what is the difference between the two theories of boltzmann and clausius stated on entropy?

The Clausius statement's: It's impossible for any system to operate in such a way that the sole result would be an energy transfer by heat from a cooler to a hotter body.

Another Clausius statement is Clausius's inequality.

∫(dQ/T)b ≤ 0

Theory of Boltzmann: Any process that increases the number of possible microscopic states of a system increases the number of possible microscopic states of a system increase its entropy, and conversely.

S = K ln w

Clausius statement is a case for any system with irreversible or reversible processes viewed macroscopically. Macroscopically because the irreversibilities count by determined its heat transfer amount. We can concluded that Clausius statement do not related to microscopical point of view, it only seen heat transfer of system at macroscopic level.

However system may change its' microscopic level by movement of the particles, but may appears to be unchanging viewed macroscopically. Accordingly, a vast number of possible microscopic states correspond to any given macroscopic equilibrium state. The total number o microscopic states available to a system is called thermodynamic probability, w. This probability related to Boltzmann relation, S = k ln w.