Soft bounds on diffusion produce skewed distributions and Gompertz growth

Salvatore Mandrà, Marco Cosentino Lagomarsino, and Marco Gherardi
Phys. Rev. E 90, 032805 – Published 12 September 2014

Abstract

Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the increments of the diffusing variable are subject to configuration-dependent bounds. This work explores theoretically some of the revealing landmarks of such phenomenology, termed “soft bound.” At long times, the system reaches a steady state irreversibly (i.e., violating detailed balance), characterized by a skewed “shoulder” in the density distribution, and by a net local probability flux, which has entropic origin. The largest point in the support of the distribution follows a saturating dynamics, expressed by the Gompertz law, in line with empirical observations. Finally, we propose a generic allometric scaling for the origin of soft bounds. These findings shed light on the impact on a system of such “scaling” constraint and on its possible generating mechanisms.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 20 May 2014

DOI:https://doi.org/10.1103/PhysRevE.90.032805

©2014 American Physical Society

Authors & Affiliations

Salvatore Mandrà1,2,3, Marco Cosentino Lagomarsino4,5, and Marco Gherardi2,3

  • 1Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge Massachusetts, USA
  • 2Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy
  • 3Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy
  • 4Sorbonne Universités, UPMC Univ Paris 06, UMR 7238, Computational and Quantitative Biology, 15 rue de l'École de Médecine Paris, France
  • 5CNRS, UMR 7238, Paris, France

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 90, Iss. 3 — September 2014

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×