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Dynamics of systems with varying number of particles: from Liouville equations to general master equations for open systems
by Mauricio J. del Razo and Luigi Delle Site
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Mauricio del Razo |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202408_00006v1 (pdf) |
| Date submitted: | 2024-08-08 15:02 |
| Submitted by: | del Razo, Mauricio |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology; ranging from the exchange of energy and matter with the surrounding environment to the change of particle numbers through internal dynamics such as reactions. The physico-mathematical modeling of these systems is extremely challenging, with the major difficulty being the time dependence of the number of degrees of freedom and the additional constraint that the increment or reduction of the number and species of particles must not violate basic physical laws. Theoretical models, in such a case, represent the key tool for the design of computational strategies for numerical studies that deliver trustful results. In this manuscript, we discuss complementary physico-mathematical approaches of varying numbers of particles inspired by different specific numerical goals. Based on the underlying structure of these models, we formulate a unifying master equation for general dynamical systems with varying numbers of particles. This equation not only embeds all the previous models but enables modeling a much larger range of complex systems ranging from molecular to social agent-based dynamics.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1- This manuscript is well written and the ideas are clearly presented.
2- The content is interesting and should be accessible to a wide readership.
3- This work has a high potential for impact in a diverse range of areas.
Report
In the manuscript entitled "Dynamics of systems with varying number of particles: from Liouville equations to general master equations for open systems" the authors synthesise a broad class of dynamics formalisms for systems with a variable number of particles using the master equation formalism. This area is historically a very difficult area to make progress in terms of achieving accurate, low-cost numerical algorithms, that can handle the varying number of particles. It is shown that, under the appropriate conditions, their formalism yields the established evolution equations in a number of important cases. Moreover the generality of their novel formalism offers the potential for new pathways to develop practical/numerical methods to treat the dynamics of 'grand canonical' type systems.
From my perspective the submitted manuscript meets the Journal's acceptance criteria: it is well written, the ideas are clearly presented, and there a high potential for impact in a diverse range of areas. I support acceptance as is.
Recommendation
Publish (meets expectations and criteria for this Journal)
Report
See attached file (First_comments.pdf)
Recommendation
Ask for major revision
Author: Mauricio del Razo on 2024-11-06 [id 4936]
(in reply to Report 2 on 2024-10-28)We are pleased to read about the positive assessment of our manuscript. The reviewer grasped the essence of our work and recognized the key ideas we aimed to communicate.