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Molecular simulations of water and ion transport through nanoporous membranes
Published in Alberto Figoli, Jan Hoinkis, Sacide Alsoy Altinkaya, Jochen Bundschuh, Application of Nanotechnology in Membranes for Water Treatment, 2017
Richard Renou, Minxia Ding, Haochen Zhu, Aziz Ghoufi, Anthony Szymczyk
An MD simulation generates information at the microscopic level (the atomic positions and the velocities of the different atoms in the system). The conversion of this microscopic information to macroscopic observables such as pressure, heat capacity, etc., can be achieved thanks to statistical mechanics. The macroscopic quantities have different forms of expression depending on the specific statistical ensemble (in which a number of the system parameters are set). The most common statistical ensembles considered in molecular simulations are: Microcanonical ensembles (NVE): a system with a fixed number of particles N, a fixed volume V, and a fixed energy E. It corresponds to an isolated system.Canonical ensembles (NVT): a system with a fixed number of particles N, a fixed volume V, and a constant temperature T.Grand canonical ensembles (µVT): a system with a constant chemical potential µ, a fixed volume V, and a constant temperature T. The system is an extension of the canonical ensemble, allowing fluctuation in the number of particles.Isothermal-isobaric ensembles (NPT): a system with a fixed number of particles N, a fixed pressure P, and a constant temperature T. This ensemble plays an important role in chemistry, as many chemical processes are carried out under conditions of constant pressure.
Atomic-Scale Simulation of Tribological and Related Phenomena
Published in Bharat Bhushan, Handbook of Micro/Nano Tribology, 2020
Judith A. Harrison, Steven J. Stuart, Donald W. Brenner
Without specific reasons to do otherwise, it is quite natural to keep the number of atoms (N) and the volume of the simulation cell (V) constant over the course of a MD simulation. In addition, for a system without energy transfer, integrating the equations of motion (Equation 11.1) will generate a trajectory over which the energy of the system (E) will also be conserved. A simulation of this type is thus performed in the constant-NVE, or microcanonical, ensemble.
The paradigm of complex probability and Ludwig Boltzmann's entropy
Published in Systems Science & Control Engineering, 2018
If all the microstates are equiprobable (a microcanonical ensemble), the statistical thermodynamic entropy reduces to the form, as given by Boltzmann: where Ω is the number of microstates, that is the number of microstates that corresponds to the macroscopic thermodynamic state. Therefore S depends on temperature. If all the messages are equiprobable, the information entropy reduces to the Hartley entropy: where is the cardinality of the message space M.