Clausius theorem

The Clausius theorem (1855) states that for a system exchanging heat with external reservoirs and undergoing a cyclic process (i.e. a process which ultimately returns a system to its original state):

where δ is the amount of heat absorbed by the system from the reservoir and is the temperature of the external reservoir at a particular instant. The equality holds in the reversible case and the inequality holds in the irreversible case. The reversible case is used to introduce the entropy state function. This is because in cyclic process the variation of a state function is zero.