Clausius statement
Heat does not pass spontaneously from a colder body to a hotter one.
Definition
The Clausius statement of the second law asserts that no process is possible whose sole result is the transfer of heat from a colder body to a hotter one. Heat left to itself always flows downhill in temperature; the reverse never happens spontaneously.
The qualifier 'sole result' is essential. A refrigerator or heat pump does move heat from cold to hot, but only by consuming work and warming its surroundings more than it cools its interior. Remove the work input and the uphill flow stops; there is no machine that carries heat from cold to hot for free.
The Clausius statement is logically equivalent to the Kelvin–Planck statement: a violation of either can be wired into a violation of the other, so forbidding one forbids both.
History
Rudolf Clausius gave this formulation in 1850 in the paper that launched the mathematical theory of the second law, capturing in a single sentence the directional asymmetry Carnot had relied upon a generation earlier.