Computational Implementation of Maxwell’s Knudsen-Gas Demon and Its Extension to a Two-Dimensional Soft-Disk Fluid
Hoover William G. *, Hoover Carol G.
Ruby Valley Research Institute
601 Highway Contract 60
Ruby Valley, Nevada 89833, USA∗E-mail: hooverwilliam@yahoo.com
Received:
Received: 25 December 2021; revised: 1 January 2022; accepted: 3 January 2022; published online: 11 January 2022
DOI: 10.12921/cmst.2021.0000035
Abstract:
An interesting preprint by Puru Gujrati, “Maxwell’s Demon Must Remain Subservient to Clausius’ Statement” [of the Second Law of Thermodynamics], traces the development and application of Maxwell’s Demon. He argues against the Demon on thermodynamic grounds. Gujrati introduces and uses his own version of a generalized thermodynamics in his criticism of the Demon. The complexity of his paper and the lack of any accompanying numerical work piqued our curiousity. The internet provides well over two million “hits” on the subject of “Maxwell’s Demon”. There are also hundreds of images of the Demon, superimposed upon a container of gas or liquid. However, there is not so much along the lines of simulations of the Demonic process. Accordingly, we thought it useful to write and execute relatively simple FORTRAN programs designed to implement Maxwell’s low-density model and to develop its replacement with global Nosé-Hoover or local purely-Newtonian thermal controls. These simulations illustrate the entropy decreases associated with all three types of Demons.
Key words:
Dense-Fluid Demon, entropy, Maxwell’s Knudsen-Gas Demon, Nosé-Hoover Demon
References:
[1] P. Gujrati, Maxwell’s Demon Must Remain Subservient to Clausius’ Statement, arXiv 2112.12300 (2021).
[2] W.G. Hoover, H.A. Posch, Large-System Hydrodynamic Limit, Mol. Phys. Rep. 10, 70–85 (1995).
[3] W.G. Hoover, Canonical Dynamics; Equilibrium Phase-Space Distributions, Phys. Rev. A 31, 1695–1697 (1985).
[4] S. Nosé, A Molecular Dynamics Method for Simulations in the Canonical Ensemble, Mol. Phys. 52, 255–268 (1984).
[5] S. Nosé, A Unified Formulation of the Constant Temperature Molecular Dynamics Methods, J. Chem. Phys. 81, 511–519 (1984).
[6] B.L. Holian, Simulations of Vibrational Relaxation in Dense Molecular Fluids. II. Generalized Treatment of Thermal Equilibration Between a Sample and a Reservoir, J. Chem. Phys. 117, 1173–1180 (2002).
[7] B.L. Holian, Evaluating Shear Viscosity: Power Dissipated Versus Entropy Produced, J. Chem. Phys. 117, 9567–9568 (2002).
An interesting preprint by Puru Gujrati, “Maxwell’s Demon Must Remain Subservient to Clausius’ Statement” [of the Second Law of Thermodynamics], traces the development and application of Maxwell’s Demon. He argues against the Demon on thermodynamic grounds. Gujrati introduces and uses his own version of a generalized thermodynamics in his criticism of the Demon. The complexity of his paper and the lack of any accompanying numerical work piqued our curiousity. The internet provides well over two million “hits” on the subject of “Maxwell’s Demon”. There are also hundreds of images of the Demon, superimposed upon a container of gas or liquid. However, there is not so much along the lines of simulations of the Demonic process. Accordingly, we thought it useful to write and execute relatively simple FORTRAN programs designed to implement Maxwell’s low-density model and to develop its replacement with global Nosé-Hoover or local purely-Newtonian thermal controls. These simulations illustrate the entropy decreases associated with all three types of Demons.
Key words:
Dense-Fluid Demon, entropy, Maxwell’s Knudsen-Gas Demon, Nosé-Hoover Demon
References:
[1] P. Gujrati, Maxwell’s Demon Must Remain Subservient to Clausius’ Statement, arXiv 2112.12300 (2021).
[2] W.G. Hoover, H.A. Posch, Large-System Hydrodynamic Limit, Mol. Phys. Rep. 10, 70–85 (1995).
[3] W.G. Hoover, Canonical Dynamics; Equilibrium Phase-Space Distributions, Phys. Rev. A 31, 1695–1697 (1985).
[4] S. Nosé, A Molecular Dynamics Method for Simulations in the Canonical Ensemble, Mol. Phys. 52, 255–268 (1984).
[5] S. Nosé, A Unified Formulation of the Constant Temperature Molecular Dynamics Methods, J. Chem. Phys. 81, 511–519 (1984).
[6] B.L. Holian, Simulations of Vibrational Relaxation in Dense Molecular Fluids. II. Generalized Treatment of Thermal Equilibration Between a Sample and a Reservoir, J. Chem. Phys. 117, 1173–1180 (2002).
[7] B.L. Holian, Evaluating Shear Viscosity: Power Dissipated Versus Entropy Produced, J. Chem. Phys. 117, 9567–9568 (2002).
