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  • Title: Coefficient of performance under maximum χ criterion in a two-level atomic system as a refrigerator.
    Author: Yuan Y, Wang R, He J, Ma Y, Wang J.
    Journal: Phys Rev E Stat Nonlin Soft Matter Phys; 2014 Nov; 90(5-1):052151. PubMed ID: 25493783.
    Abstract:
    A two-level atomic system as a working substance is used to set up a refrigerator consisting of two quantum adiabatic and two isochoric processes (two constant-frequency processes ω_{a} and ω_{b} with ω_{a}<ω_{b}), during which the two-level system is in contact with two heat reservoirs at temperatures T_{h} and T_{c}(<T_{h}). Considering finite-time operation of two isochoric processes, we derive analytical expressions for cooling rate R and coefficient of performance (COP) ɛ. The COP at maximum χ(=ɛR) figure of merit is numerically determined, and it is proved to be in nice agreement with the so-called Curzon and Ahlborn COP ɛ_{CA}=sqrt[1+ɛ_{C}]-1, where ɛ_{C}=T_{c}/(T_{h}-T_{c}) is the Carnot COP. In the high-temperature limit, the COP at maximum χ figure of merit, ɛ^{*}, can be expressed analytically by ɛ^{*}=ɛ_{+}≡(sqrt[9+8ɛ_{C}]-3)/2, which was derived previously as the upper bound of optimal COP for the low-dissipation or minimally nonlinear irreversible refrigerators. Within the context of irreversible thermodynamics, we prove that the value of ɛ_{+} is also the upper bound of COP at maximum χ figure of merit when we regard our model as a linear irreversible refrigerator.
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