Netz, R.R. (2017) Fluctuationdissipation relation and stationary distribution for an exactly solvable manyparticle model far from equilibrium. SFB 1114 Preprint 12/2017 . (Unpublished)

PDF
496kB 
Abstract
An exactly solvable, Hamiltonianbased model of many massive particles that are coupled by harmonic potentials and driven by stochastic nonequilibrium forces is introduced. The stationary distribution as well as the fluctuationdissipation relation are derived in closed form for the general nonequilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution, which is possible because the model derives from a particle Hamiltonian. The difference between the obtained nonequilibrium fluctuationdissipation relation and the standard equilibrium fluctuationdissipation theorem allows to quantify nonequilibrium in an alternative fashion. Both indicators of nonequilibrium behavior, i.e. deviations from the Boltzmann distribution and deviations from the equilibrium fluctuationdissipation theorem, can be expressed in terms of a single nonequilibrium parameter \alpha that involves the ratio of friction coefficients and random force strengths. The concept of a nonequilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to closetoequilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from nonlinear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates, the obtained results should thus be quite general. This is demonstrated by comparison of the derived nonequilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energyconsuming protein motors. The comparison is excellent and allows to extract the nonequilibrium parameter \alpha from experimental spectral response and fluctuation data.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
ID Code:  2227 
Deposited By:  Silvia Hoemke 
Deposited On:  21 Feb 2018 11:18 
Last Modified:  22 Feb 2018 13:35 
Repository Staff Only: item control page