Clausius statement (according to Wikipedia):
No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.
Clausius equality:
$$\oint \frac{\delta Q}{\theta} = 0$$ (which implies existence of entropy $S$: $dS = \frac{\delta Q}{\theta}$)
They both are the statements of the second law of thermodynamics. How to prove their equivalence? This prove seems to be frequently omitted from books, I don't know why.
Frankly speaking, Clausius statement may be easily derived from Clausius equality. The question is derivation of the equality from the statement.
