Transport Properties in Non-Equilibrium and Anomalous by Dario Villamaina

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By Dario Villamaina

The examine of fluctuations in statistical physics has an extended heritage, and a normal conception is definitely verified, connecting fluctuations to reaction homes of equilibrium platforms. Remarkably, this framework fails once a few present is flowing around the approach, using it out of equilibrium.
The presence of currents is very common in nature and produces wealthy phenomena that are faraway from being integrated in a basic framework. This thesis specializes in this common challenge through learning various types similar to granular fabrics and platforms displaying anomalous diffusion and exhibits how the generalized reaction innovations could be effectively used to capture the proper levels of freedom that force the platforms out of equilibrium.
This research paves tips on how to using the generalized fluctuation family in an operative manner, with a purpose to extract info from a non-equilibrium process and to construct the corresponding phenomenological theory.

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3 An Example of Out of Equilibrium Systems: The Granular Gases 25 which is a quite involved function of the parameters, as we will see in the next section. In this model is possible to recover two different regimes: τb grains thermalize, on average, with the bath before experiencing • When τc a collision and the inelastic effects are negligible. This is an “equilibrium-like” regime, similar to the elastic case r = 1, where the granular gas is spatially homogeneous, the distribution of velocity is Maxwellian and Tg = Tb .

Stat. Mech. P09013 (2005) References 33 87. : Is it possible to experimentally verify the fluctuation relation? a review of theoretical motivations and numerical evidence. J. Stat. Mech. P02008 (2007) 88. : Nonequilibrium statistical mechanics. Oxford University Press, Oxford (2001) 89. : Time-correlation functions and transport coefficients in statistical mechanics. Ann. Rev. Phys. Chem. 16, 67 (1965) Chapter 3 The Effects of Memory on Linear Response and Entropy Production Abstract In this chapter the Langevin equation with memory is analyzed in both equilibrium and non equilibrium setups.

Similar considerations can be proposed also for the overdamped case. The only difference is that, since the observables are positions, one must compare the response matrix with the derivative of the autocorrelation. By deriving respect to time Eq. 53) where, in this case Aσ = − T T T2 γ2 46 3 The Effects of Memory on Linear Response and Entropy Production k with = (k+k2 )γ2 +(k+k and, as usual T = (T1 − T2 ). The similarity with 1 )γ1 Eq. 48) is now explicit: when T1 = T2 , also in this case, (Aσ )12 vanishes and one ˙ recovers the known fluctuation dissipation relation R(t) ∝ C(t).

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