Breakdown of the Onsager Principle as a Sign of Aging

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Article discussing the breakdown of the Onsager principle as a sign of aging.

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11 p.

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Allegrini, Paolo; Aquino, Gerardo; Grigolini, Paolo; Palatella, Luigi & Rosa, Angelo July 19, 2011.

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Article discussing the breakdown of the Onsager principle as a sign of aging.

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11 p.

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This is the pre-print version of the paper, reprinted with permission from American Physical Society. The final definitive version is available here: http://link.aps.org/doi/10.1103/PhysRevE.68.056123

Abstract: We discuss the problem of the equivalence between Continuous Time Random Walk (CTRW) and Generalized Master Equation (GME). The walker, making instantaneous jumps from one site of the lattice to another, resides in each site or extended time. The sojourn times have a distribution ψ (t) that is assumed to be an inverse power law with the power index μ. We assume that the Onsager principle is fulfilled, and we use this assumption to establish a complete equivalence between GME and the Montroll-Weiss CTRW. We prove that this equivalence is confined to the case when ψ (t) is an exponential. We argue that is so because the Montroll-Weiss CTRW, as recently proved by Barkai [E. Barkai, Phys. Rev. Lett. 90, 104101 (2003)], is non-stationary, thereby implying aging, while the Onsager principle, is valid only in the case of fully aged systems. The case of Poissonian distribution of sojourn times is the only one with no aging associated to it, and consequently with no need to establish special initial conditions to fulfill the Onsager principle. We consider the case of a dichotomous fluctuation, and we prove that the Onsager principle is fulfilled for any form of regression to equilibrium provided that the stationary condition hold true. We set the stationary condition on both the CTRW and the GME, thereby creating a condition of total equivalence, regardless the nature of the waiting time distribution. As a consequence of this procedure we create a GME that is a bona fide master equation, in spite of being non-Markovian. We note that the memory kernel of the GME affords information on the interaction between system of interest and its bath. The Poisson case yields a bath with infinitely fast fluctuations. We argue that departing from the Poisson form has the effect of creating a condition of infinite memory and that these results might be useful to shed light into the problem of how to unravel non-Markovian master equations.

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  • Physical Review E, 2003, College Park: American Physical Society

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  • Publication Title: Physical Review E
  • Volume: 68
  • Issue: 5
  • Pages: 11
  • Peer Reviewed: Yes

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  • July 19, 2011

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  • July 24, 2013, 1:20 p.m.

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  • March 27, 2014, 3:23 p.m.

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Allegrini, Paolo; Aquino, Gerardo; Grigolini, Paolo; Palatella, Luigi & Rosa, Angelo. Breakdown of the Onsager Principle as a Sign of Aging, article, July 19, 2011; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc174692/: accessed September 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.