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.
Soft bounds on diffusion produce skewed distributions and Gompertz growth / S. Mandrà, M. Cosentino Lagomarsino, M. Gherardi. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 90:3(2014), pp. 032805.1-032805.8.
Titolo: | Soft bounds on diffusion produce skewed distributions and Gompertz growth |
Autori: | MANDRA', SALVATORE (Primo) COSENTINO LAGOMARSINO, MARCO (Secondo) GHERARDI, MARCO (Ultimo) |
Parole Chiave: | Condensed Matter Physics; Statistical and Nonlinear Physics; Statistics and Probability |
Settore Scientifico Disciplinare: | Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici |
Data di pubblicazione: | 2014 |
Rivista: | |
Tipologia: | Article (author) |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1103/PhysRevE.90.032805 |
Appare nelle tipologie: | 01 - Articolo su periodico |
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File | Descrizione | Tipologia | Licenza | |
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1409.5802.pdf | Pre-print (manoscritto inviato all'editore) | Open Access Visualizza/Apri | ||
PhysRevE.90.032805.pdf | Publisher's version/PDF | Open Access Visualizza/Apri |