
Physics 2005
On the Computational Power of Molecular Heat EnginesDOI: 10.1007/s1095500580159 Abstract: A heat engine is a machine which uses the temperature difference between a hot and a cold reservoir to extract work. Here both reservoirs are quantum systems and a heat engine is described by a unitary transformation which decreases the average energy of the bipartite system. On the molecular scale, the ability of implementing such a unitary heat engine is closely connected to the ability of performing logical operations and classical computing. This is shown by several examples: (1) The most elementary heat engine is a SWAPgate acting on 1 hot and 1 cold twolevel systems with different energy gaps. (2) An optimal unitary heat engine on a pair of 3level systems can directly implement OR and NOT gates, as well as copy operations. The ability to implement this heat engine on each pair of 3level systems taken from the hot and the cold ensemble therefore allows universal classical computation. (3) Optimal heat engines operating on one hot and one cold oscillator mode with different frequencies are able to calculate polynomials and roots approximately. (4) An optimal heat engine acting on 1 hot and n cold 2level systems with different level spacings can even solve the NPcomplete problem KNAPSACK. Whereas it is already known that the determination of ground states of interacting manyparticle systems is NPhard, the optimal heat engine is a thermodynamic problem which is NPhard even for n noninteracting spin systems. This result suggest that there may be complexitytheoretic limitations on the efficiency of molecular heat engines.
