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Evaluation of entropy via Molecular Dynamics: recent advancements and challenges

Mercoledì 10 luglio alle ore 11:00 in aula Zironi, edificio Matematica, Dipartimento FIM, Modena

Relatore: Prof. Federico Frascoli (Swinburne University of Technology)

Abstract: Given that the Gibbs' expression for the entropy of an ensemble of interacting particles can be problematic when the system is driven out of equilibrium, an alternative approach, namely the so-called Green’s expansion, can be used to calculate such quantity. The formula is accurate but generally demands a large amount of computational resources and is extremely sensitive to numerical error even in the case of systems at equilibrium. Further, in its original formulation, the computation is not straightforward and difficult to implement.
A new and more elegant method for the computation of the Green’s formula has been recently been developed and is discussed in this talk, with application to the evaluation of the first three order terms in the expansion. For systems at equilibrium, the method gives good agreement with the available literature for fluid samples at low density. At higher densities, an anomalous and spurious drift of the entropy emerges, making the entropy diverge from its true asymptotic value. This drift is analysed for various systems of WCA particles in different macroscopic conditions, and a procedure to eliminate it is presented. Final remarks on the extensions of these results for higher order terms and for nonequilibrium ensembles complete the presentation.

Biodata: Federico Frascoli is an Associate Professor in Applied Mathematics at Swinburne University of Technology, Melbourne. He is interested in systems out of equilibrium, in a variety of (apparently) different contexts. From cellular motility to nano-confined fluids, from immune-cancer dynamics to brain oscillations, his research is focussed on patterns and strategies that Nature creates far from equilibrium. Questions that arise in these situations embrace a number of different areas of applied mathematics and mathematical physics, ranging from statistical mechanics, non equilibrium thermodynamics and classical molecular dynamics to dynamical systems, bifurcation theory, PDEs, ODEs and agent-based modeling techniques.

[Ultimo aggiornamento: 01/04/2021 12:01:00]