Repository: Freie Universit├Ąt Berlin, Math Department

Derivation of Liouville-like equation for the n-state probability density of an open system with thermalized particle reservoirs and its link to molecular simulation

Delle Site, L. and Klein, R. (2022) Derivation of Liouville-like equation for the n-state probability density of an open system with thermalized particle reservoirs and its link to molecular simulation. J. Physics A:Math. Theor., 55 (15).

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Official URL: https://iopscience.iop.org/article/10.1088/1751-81...

Abstract

A physico-mathematical model of open {systems} {proposed in a previous paper [ L.Delle Site and R.Klein, J.Math.Phys. 61, 083102 (2020)] can represent a guiding reference in designing an accurate simulation scheme for an open molecular system embedded in a reservoir of energy and particles. The derived equations and the corresponding boundary conditions are obtained without assuming the action of an external source of heat that assures thermodynamic consistency of the open system with respect to a state of reference. However, in numerical schemes the temperature in the reservoir must be controlled by an external heat bath otherwise thermodynamic consistency cannot be achieved. In this perspective, the question to address is whether the explicit addition of an external heat bath in the theoretical model modifies the equations of the open system and its boundary conditions. In this work we consider this aspect and explicitly describe the evolution of the reservoir employing the Bergmann-Lebowitz statistical model of thermostat. It is shown that the resulting equations for the open system itself are not affected by this change and an example of numerical application is reviewed where the current result shows its conceptual relevance.} Finally, a list of pending mathematical and modelling problems is discussed the solution of which would strengthen the mathematical rigour of the model and offer new perspectives for the further development of a new multiscale simulation scheme.

Item Type:Article
Additional Information:Open access
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2841
Deposited By: Ulrike Eickers
Deposited On:22 Aug 2022 14:02
Last Modified:25 Aug 2022 14:04

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