Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany.
Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-180 00 Praha, Czech Republic.
Phys Rev E. 2017 Sep;96(3-1):030102. doi: 10.1103/PhysRevE.96.030102. Epub 2017 Sep 6.
We investigate fluctuations of output work for a class of Stirling heat engines with working fluid composed of interacting units and compare these fluctuations to an average work output. In particular, we focus on engine performance close to a critical point where Carnot's efficiency may be attained at a finite power as reported by M. Campisi and R. Fazio [Nat. Commun. 7, 11895 (2016)2041-172310.1038/ncomms11895]. We show that the variance of work output per cycle scales with the same critical exponent as the heat capacity of the working fluid. As a consequence, the relative work fluctuation diverges unless the output work obeys a rather strict scaling condition, which would be very hard to fulfill in practice. Even under this condition, the fluctuations of work and power do not vanish in the infinite system size limit. Large fluctuations of output work thus constitute inseparable and dominant element in performance of the macroscopic heat engines close to a critical point.
我们研究了一类由相互作用单元组成的工质的斯特林热机的输出功涨落，并将其与平均功输出进行了比较。特别是，我们关注了接近临界点的发动机性能，正如 M. Campisi 和 R. Fazio [Nat. Commun. 7, 11895 (2016)2041-172310.1038/ncomms11895] 报道的那样，在临界点附近，卡诺效率可以在有限的功率下达到。我们表明，每个循环的功输出方差与工质的热容具有相同的临界指数。因此，除非输出功遵守相当严格的标度条件，否则相对功涨落将发散，而在实际中这将很难满足。即使在这种情况下，功和功率的涨落也不会在无限大系统尺寸极限下消失。因此，在接近临界点的宏观热机性能中，输出功的大幅涨落是不可分割且占主导地位的因素。
