"We proceed now to the consideration of non-reversible cyclical processes. ...[W]e obtain the following theorem, which applies generally to all cyclical processes, those that are reversible forming the limit:—The algebraical sum of all [non-reversible] transformations occurring in a cyclical process can only be positive."
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Note: reversible processes would be strictly hypothetical, so the above statement actually pertains to all real transformations occurring in a cyclical process.
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Rudolf Clausius
Rudolf Julius Emanuel Clausius (2 January 1822 –24 August 1888) was a German physicist and mathematician. He is considered one of the founders of the science of thermodynamics. By his restatement of Sadi Carnot's principle known as the Carnot cycle, he provided a more fundamental foundation for the theory of heat. His most important paper, On the Moving Force of Heat (1850) was first to declare the second law of thermodynamics. He introduced the concept of entropy in 1865, and the virial theorem
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