1009.2536v1 - Maximally ecient quantum thermal machines The...

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arXiv:1009.2536v1 [quant-ph] 13 Sep 2010 Maximally efficient quantum thermal machines: The basic principles Sandu Popescu H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom (Dated: September 15, 2010) Following the result by Skrzypczyk et al., arXiv:1009.0865, that certain self-contained quantum thermal machines can reach Carnot efficiency, we discuss the functioning of self-contained quantum thermal machines and show, in a very general case, that they can reach the Carnot efficiency limit. Most importantly, the full analytical solution for the functioning of the machines is not required; the efficiency can be deduced from a very small number of fundamental and highly intuitive equations which capture the core of the problem. In a very recent work [1] two fundamental questions were raised about thermal machines. The first question was whether or not there exists a fundamental limita- tion to the size of (quantum) thermal machines (where size is measured in the number of quantum states the ma- chine). The second question refers to the efficiency of the machines: is there any complementarity between size and efficiency? That is, can the Carnot efficiency be reached by machines with only very few quantum states? The first question was answered in [1] where the smallest re- frigerator was designed: there is effectively no lower limit on the number of states. The second question was an- swered in [2] where it was shown that there is no trade-off between size and efficiency and that the smallest possible refrigerator can reach the Carnot limit. The results in [2] however are based on rather compli- cated computations, involving solving for the exact ana- lytical solution. All these computation mysteriously sim- plify in the end. Here we revisit the problem and show that finding the entire analytical solution (which depends on all the parameters of the problem and on the details of the interaction with the environment) is not neces- sary. Instead we formulate main principles that govern the functioning of our quantum thermal machines; these principles capture the core of the problem and lead to the Carnot efficiency in a clear, straightforward and very intuitive manner. Obviously, the above results do not come into a vac- uum. During the last couple of years there has been a lot of interest in the functioning of quantum thermal ma- chines [4]-[24], with major results being obtained. Here however we are specifically interested in accounting for all the degrees of freedom of the machine, for all its states. Hence we are considering fully self-contained machines and we do not allow, explicitly or implicitly, for any ex- ternal source of work. In particular, we do not allow for time dependent Hamiltonians or prescribed unitary transformations. All that our machines are allowed is access to heat baths.
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