Towards the thermodynamics of localization processes

Grigolini, Paolo; Pala, Marco; Palatella, Luigi; Roncaglia, Roberto

doi:10.1103/physreve.62.3429

Cited by 12 publications

(14 citation statements)

References 25 publications

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“…This approach implies the adoption of a reduced density matrix, and consequently of the GME that one can derive from a Liouville equation, via the adoption of a convenient projection method (see, for instance, Ref. [31]). We have adopted, on the contrary, a picture based on the assumption of the existence of real trajectories.…”

Section: Discussionmentioning

confidence: 99%

Absorption and emission in the non-poisson case: the theoretical challenge posed by renewal aging

Aquino

Palatella²,

Grigolini³

2005

Braz. J. Phys.

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This short paper aims at clarifying the physical meaning of a previous pubblication [G. Aquino, P. Grigolini, L. Palatella, Phys. Rev. Lett. 93 050601 (2004)], using later, although very recent, results. This has to do with the challenges posed to the Kubo-Anderson (KA) theory, and more in general to any form of Liouville-like approach, by the discovery of intermittent resonant fluorescence with a non-exponential distribution of waiting times. We show that to properly address the treatment of these problems the KA theory, valid in the case of aged systems, should be extended to aging systems, aging for a very extended time period or even forever, being a crucial consequence of non-Poisson statistics. This ambitious goal can be realized if we adopt the assumption that real wave-function collapses occur.

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Section: Discussionmentioning

confidence: 99%

Absorption and emission in the non-poisson case: the theoretical challenge posed by renewal aging

Aquino

Palatella²,

Grigolini³

2005

Braz. J. Phys.

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“…We are now equipped to adopt the Zwanzig projection method [30]. The projection operator P works according to the following prescription P φ(x, y, t) = σ(x, t)η(y).…”

Section: Appendix: Frobenius-perron Operator For An Idealized Model Omentioning

confidence: 99%

Strange kinetics: conflict between density and trajectory description

2002

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We study a process of anomalous diffusion, based on intermittent velocity fluctuations, and we show that its scaling depends on whether we observe the motion of many independent trajectories or that of a Liouville-like equation driven density. The reason for this discrepancy seems to be that the Liouville-like equation is unable to reproduce the multi-scaling properties emerging from trajectory dynamics. We argue that this conflict between density and trajectory might help us to define the uncertain border between dynamics and thermodynamics, and that between quantum and classical physics as well.

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“…55 This becomes rapidly more cumbersome as the order of the expansion is increased. A more convenient expansion of the memory kernel is to first expand the Green's function in Eq.…”

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confidence: 99%

Microscopic theory of protein folding rates. II. Local reaction coordinates and chain dynamics

Portman

Takada

Wolynes

2001

The Journal of Chemical Physics

159

196

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The motion involved in barrier crossing for protein folding are investigated in terms of the chain dynamics of the polymer backbone, completing the microscopic description of protein folding presented in the previous paper. Local reaction coordinates are identified as collective growth modes of the unstable fluctuations about the saddle-points in the free energy surface. The description of the chain dynamics incorporates internal friction (independent of the solvent viscosity) arising from the elementary isomerizations of the backbone dihedral angles. We find that the folding rate depends linearly on the solvent friction for high viscosity, but saturates at low viscosity because of internal friction. For λ-repressor, the calculated folding rate prefactor, along with the free energy barrier from the variational theory, gives a folding rate that agrees well with the experimentally determined rate under highly stabilizing conditions, but the theory predicts too large a folding rate at the transition midpoint. This discrepancy obtained using a fairly complete quantitative theory inspires a new set of questions about chain dynamics, specifically detailed motions in individual contact formation.

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Towards the thermodynamics of localization processes

Cited by 12 publications

References 25 publications

Absorption and emission in the non-poisson case: the theoretical challenge posed by renewal aging

Absorption and emission in the non-poisson case: the theoretical challenge posed by renewal aging

Strange kinetics: conflict between density and trajectory description

Microscopic theory of protein folding rates. II. Local reaction coordinates and chain dynamics

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