| 872 | 0 | 20 |
| 下载次数 | 被引频次 | 阅读次数 |
麦克斯韦妖的提出是为了表明热力学第二定律可能有问题，但这可以通过引入信息熵解决。本文从统计的角度研究了两种简单的麦克斯韦妖系统的最小熵变随时间的变化关系。第一种模型的冷热分子的速度分别相等；第二种模型包含两种分子量的分子，每种分子都满足麦克斯韦速度分布律。通过概率论的方法，研究了系统的热力学熵、信息熵以及总熵的变化情况。系统熵变的理论结果能够得到定量的解释，无需引入任何待定参量或者模拟数据。同时，我们也讨论了不同条件下的系统熵变的情况。所得到的理论结果和模拟数据完全相符。
Abstract：Maxwell's demon system seems to violate the second law of thermodynamics. The problem is solved by introducing the information entropy. This paper introduces two simple models for the Maxwell's demon system to study the least entropy change in the sense of statistic. In the first model, the velocities of hot and cold molecules are equal respectively. The second model contains two molecules with different molecular weights, each of which satisfies Maxwell's velocity distribution law. The changes of thermodynamic entropy, the information entropy and the total entropy are studied in probability theory. The theoretical results are quantitative, without any undetermined parameters and also confirm the simulation data. The entropy changes in different conditions are also discussed. The theoretical results are in good agreement with the simulated data.
[1] DAUB E E.Maxwell's demon[J].Studies in History and Philosophy of Science Part A,1970,1(3):213-227.
[2] KOSKI J V,PEKOLA J P.Maxwell's demons realized in electronic circuits[J].Comptes Rendus Physique,2016,17(10):1130-1138.
[3] GYFTOPOULOS E P.Maxwell's demon.(I) A thermodynamic exorcism[J].Physica A,2002,307(3):405-420.
[4] SZILARD L.On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings[J].Behavioral Science,1929,9(4):301-310.
[5] SHANNON C.A mathematical theory of communication[J].The Bell System Technical Journal,1948,27(3):379-423.
[6] CAMATI P A,PETERSON J P,BATALH?O T B,et al.Experimental rectication of entropy production by Maxwell's demon in a quantum system[J].Physical Review Letters,2016,117:240502.
[7] NAGHILOO M,ALONSO J,ROMITO A,et al.Information gain and lossfor a quantum Maxwell's demon[J].Physical Review Letters,2018,121:030604.
[8] MASUYAMA Y,FUNO K,MURASHITA Y,et al.Information-to-workconversion by Maxwell's demon in a superconducting circuit quantum electrodynamical system[J].Nature Communications,2018,9:1291.
[9] WANGWB,CHANG X Y,WANG F,et al.Supplemental materials:Realizationof quantum Maxwell's demon with solid-state spins[J].Chinese Physics Letters,2018,35:12-14.
[10] HOSSENFELDER S.The remote maxwell demon as energy down converter[J].Springer,2016,46:505-516.
[11] SKORDOS P,ZUREK W.Maxwell's demon,rectiers,and the secondlaw:Computer simulation of Smoluchowski' strapdoor[J].American Journal of Physics,1992,60:876.
[12] BUB J.Maxwell's demon and the thermodynamics of computation[J].Pergamon,2001,32(4):569-579.
[13] HONDOU T.Equation of state in a small system:Violation of an assumption of Maxwell's demon[J].EPL (Europhysics Letters),2007,80(5):50001.
[14] D'ABRAMO G.The peculiar status of the second law of thermodynamics and the quest for its violation[J].Studies in the History and Philosophy of Modern Physics,2012,43:226-235.
[15] NIELSEN M A,CHUANG I L.Quantum computation and quantuminformation[M].Cambridge:Cambridge University Press,2010.
[16] PALAZZO P.Hierarchical structure of generalized thermodynamic and informational entropy[J].Entropy,2018,20:553.
[17] PAPOULIS A,PILLAI S U.Probability,Random variables,and StochasticProcesses[M].New York:McGraw-Hill,2002.
[18] LEFF H S,REX A F.Entropy of measurement and erasure:Szilard's membrane model revisited[J].American Journal of Physics,1994,62:994-1000.
[19] LANDAUER R.Irreversibility and heat generation in the computing process[J].IBM Journal of Research and Development,1961,5:183-191.
[20] BENNETT C H.Demons,engines and the second law[J].Scientic American,1987,257:108-116.
[21] MILLER R C,KUSCH P.Velocity distributions in potassium and thalliumatomic beams[J].Phys.Rev.,1955,99:1314-1321.
基本信息:
中图分类号:O414.1
引用信息:
[1]赵欣林,薛郁,蒋绍周.经典麦克斯韦妖系统中熵随时间的变化关系[J].物理与工程,2022,32(01):18-24.
基金信息:
广西自然科学基金(2018GXNSFAA281180)
2022-02-15
2022-02-15