A Monte Carlo study of Maxwell’s demon coupled to finite quantum heat baths

Abstract

When Maxwell’s demon was introduced, it raised the question: Is there a way to decrease an isolated system’s entropy, even though it was forbidden by the second law of thermodynamics. Then, a new idea which considered information as a physical entity was emerged, and an equivalence between information entropy and thermodynamic entropy was suggested. Under the light of new understandings, the original question modified into "Is there a way to decrease thermodynamic entropy of a system by using information entropy?" This work aims to demonstrate such a machinery is possible to exist in real world. Building on the model of Mandal et al. [1], it inquires whether if such a system is possible to build in nano scales. According to the theoretical relations, the correspondences between internal energy and effective temperature of finite fermionic and bosonic gases for varying number of particles and volumes were tabulated. Subsequently, a series of Monte Carlo simulations were executed under different circumstances. The outcomes of the simulations illustrate that production of information entropy can be used to compensate the decrease of thermodynamic entropy. The results indicate that using either one of the quantum gases as a finite quantum heat bath does affect the efficiency of the refrigerator. Based on this, using fermionic gas is superior to bosonic gas in terms of swiftness of the refrigeration, if all other variables are identical. Further research is needed to analyze the behaviour of the finite quantum heat baths at extremely low temperatures.