Efficiency of the general quantum-mechanical Carnot engine

A quantum-mechanical analog of the Carnot engine reversibly working at vanishing temperature, shortly termed the quantum-mechanical Carnot engine, is discussed. A general formula for the efficiency of such an engine with an arbitrary confining potential is presented. Its expression is purely given in terms of the structure of the energy spectrum. Dependency of the efficiency on the form of a potential as an analog of the working material in thermodynamics implies nonuniversality of the engine. This may be due to the absence of the second-law-like principle in pure-state quantum mechanics.