Alternative Statements of the Second Law (There are many)

Clausius

Heat is not observed to pass spontaneously from a body at low temperature to a body at higher temperature.

Kelvin

It is impossible to continuously perform work by cooling a body to a temperature below that of the lowest temperature of its surroundings.

Ostwald

A perpetual motion machine ``of the second kind'' has never been observed. (A perpetual motion machine of the second kind ``runs forever.'')¹

Caretheodory

This is the most elegant (and hardest to understand and apply, perhaps) as it requires the fewest underlying assumptions.

In the neighborhood of every thermodynamic state that can be reached by a reversible path, there exists states which cannot be reached along a reversible adiabatic (isentropic) path; or, in other words, which can be reached either irreversibly or not at all.

MIT 3.00

Entropy is a state function that exists for every physical system and has the property that, when all associated systems are consideredfootnote The universe of a process. the sum of all the entropy changes is greater than or equal to zero.