Fluctuation-dissipation relation

The fluctuation dissipation theorem relates the dissipative part of the response fiinction (x") to the correlation of fluctuations (A, for any system in themial equilibrium. The left-hand side describes the dissipative behaviour of a many-body system all or part of the work done by the external forces is irreversibly distributed mto the infinitely many degrees of freedom of the themial system. The correlation fiinction on the right-hand side describes the maimer m which a fluctuation arising spontaneously in a system in themial equilibrium, even in the absence of external forces, may dissipate in time. In the classical limit, the fluctuation dissipation theorem becomes / /., w) = w). [Pg.719]

G. N. Bochkov and Y. E. Kuzovlev, Non-linear fluctuation relations and stochastic models in nonequilibrium thermodynamics. 1. Generalized fluctuation-dissipation theorem. Physica A 106, 443-J79 (1981). [Pg.116]

As A x was supposed stationary the integral is independent of time. The effect of the fluctuations is therefore to renormalize A0 by adding a constant term of order a2 to it. The added term is the integrated autocorrelation function of At. In particular, if one has a non-dissipative system described by A0, this additional term due to the fluctuations is usually dissipative. This relation between dissipation and the autocorrelation function of fluctuations is analogous to the Green-Kubo relation in many-body systems 510 but not identical to it, because there the fluctuations are internal, rather than added as a separate term as in (2.1). [Pg.401]

The starting point for the proposed new approach is an exact formula [238], [239], based on the adiabatic connection formula and the zero-temperature fluctuation-dissipation theorem, relating the groundstate xc energy to the inter-... [Pg.159]

Over the past 15 years a number of important fundamental theorems in nonequilibrium statistical mechanics of many-particle systems have been proved. These proofs result in a number of important relations in nonequilibrium statistical mechanics. In this review we focus on three new relationships the dissipation function or Evans-Searles fluctuation relation (ES the Jarzynski equality... [Pg.181]

The first of these relations, the ES FR, is also referred to as the transient fluctuation relation (transient FR) or the dissipation function fluctuation relation (Q-FR). It gives an analytic expression for the probability that for a finite system observed for a finite time, the average of the so-called dissipation function , Qt — y/q f2(F(i ))di, takes on a positive or negative value. That is it states ... [Pg.181]

For deterministic systems, the FR takes on the form (1.1) and the dissipation function is given by (2.1). However, in the case of stochastic dynamics, the same process might be modelled at different levels with different dynamics, and for each model a different fluctuation relation may be obtained. Therefore there are more papers on stochastic systems than on deterministic dynamics, as derivations for new dynamics allow new systems to be treated. This is particularly true for the Jarzynski relation, as discussed in section 3.2. [Pg.188]

In all these experimental studies, the particle was in a viscous fluid and therefore the equations of motion of the particle were well approximated by a stochastic Langevin equation. In 2007, a capture experiment was carried out in a viscoelastic solvent where this approximation no longer applies. It was shown that despite this, the experiments validated the ES FR, and therefore could not be consider just a special property of Brownian dynamics. Blickle et a/. verified the fluctuation relation for the work (or dissipation function) for a system where the trap potential was not harmonic. [Pg.189]

In deterministic systems, it is the dissipation function that is the subject of the FR (1.1). In contrast, it has been demonstrated that for stochastic systems, there can be more than one property that satisfies a fluctuation relation. ... [Pg.195]

Here T is the local-equilibrium temperature. In extended irreversible thermodynamics fluxes are independent variables. The kinetic temperature associated to the three spatial directions of along the flow, along the velocity gradient, and perpendicular to the previous to directions may be different from each other. To define temperature from the entropy is the most fundamental definition, and the nonequilibrium temperature may come from the derivative of a nonequilibrium entropy du/dS) -p. Effective nonequilibrium temperature may be defined from the fluctuation-dissipation theorem relating response function and correlation function. [Pg.652]

The fluctuation-dissipation theorem relates the correlations to absorption in other words, the scattering function is proportional to the imaginary part of a generalised (Q and to dependent) susceptibility, In the zero-frequency, zero-wavevector... [Pg.284]

The Fluctuation-dissipation Theorem Relates Equilibrium Fluctuations to the Rate of Approach to Equilibrium... [Pg.333]

Imagine that we select within a sample a subsystem contained in a volume Vj which is small but still macroscopic in the sense that statistical thermodynamics can be applied. If we could measure the properties of this subsystem we would observe time dependent fluctuations, for example in the shape of the volume, i.e. the local strain, the internal energy, the total dipole moment, or the local stress. The fluctuation-dissipation theorem relates these spontaneous, thermally driven fluctuations to the response functions of the system. We formulate the relationship for two cases of interest, the fluctuations of the dipole moments in a polar sample and the fluctuations of stress in a melt. [Pg.257]

Thus, the requirement that the Brownian particle becomes equilibrated with the surrounding fluid fixes the unknown value of, and provides an expression for it in tenns of the friction coefficient, the thennodynamic temperature of the fluid, and the mass of the Brownian particle. Equation (A3.1.63) is the simplest and best known example of a fluctuation-dissipation theorem, obtained by using an equilibrium condition to relate the strengtii of the fluctuations to the frictional forces acting on the particle [22]. [Pg.689]

Putting (A3.2.10) into (A3.2.4) gives the prototype example of what is called the fluctuation-dissipation relation... [Pg.695]

The response fiinction H, which is defined in equation (A3.3.4), is related to the corresponding correlation fiinction, kliroiigh the fluctuation dissipation theorem ... [Pg.719]

There are tliree steps in the calculation first, solve the frill nonlinear set of hydrodynamic equations in the steady state, where the time derivatives of all quantities are zero second, linearize about the steady-state solutions third, postulate a non-equilibrium ensemble through a generalized fluctuation dissipation relation. [Pg.728]

In this equation, m. is the effective mass of the reaction coordinate, q(t -1 q ) is the friction kernel calculated with the reaction coordinate clamped at the barrier top, and 5 F(t) is the fluctuating force from all other degrees of freedom with the reaction coordinate so configured. The friction kernel and force fluctuations are related by the fluctuation-dissipation relation... [Pg.889]

Using the fluctuation-dissipation theorem [361, which relates microscopic fluctuations at equilibrium to macroscopic behaviour in the limit of linear responses, the time-dependent shear modulus can be evaluated [371 ... [Pg.2528]

The quantity k is related to the intensity of the turbulent fluctuations in the three directions, k = 0.5 u u. Equation 41 is derived from the Navier-Stokes equations and relates the rate of change of k to the advective transport by the mean motion, turbulent transport by diffusion, generation by interaction of turbulent stresses and mean velocity gradients, and destmction by the dissipation S. One-equation models retain an algebraic length scale, which is dependent only on local parameters. The Kohnogorov-Prandtl model (21) is a one-dimensional model in which the eddy viscosity is given by... [Pg.102]

Other spectral densities correspond to memory effects in the generalized Langevin equation, which will be considered in section 5. It is the equivalence between the friction force and the influence of the oscillator bath that allows one to extend (2.21) to the quantum region there the friction coefficient rj and f t) are related by the fluctuation-dissipation theorem (FDT),... [Pg.17]

Under certain conditions the energy dissipation may lead to an oscillatory regime of laminar flow in micro-channels. The relation of hydraulic diameter to channel length and the Reynolds number are important factors that determine the effect of viscous energy dissipation on flow parameters. The oscillatory flow regime occurs in micro-channels at Reynolds numbers less than Recr- In this case the existence of velocity fluctuations does not indicate change from laminar to turbulent flow. [Pg.139]

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