Fluctuation-dissipation theorems localization

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. 

The OEP method can be used to obtain the exact XC potential. In fact using the Gorling-Levy perturbation theory (GLPT) the exact XC energy can be expanded in series and each term is a functional of orbitals and eigenvalues (the first term is just the EXX energy) for eaeh term a local potential can be obtained using the OEP method. Similar expansions hold for the correlation functional based on the fluctuation-dissipation-theorem. " ... 

The noise associated with these local forces is non-thermal and, as a result, does not satisfy the fluctuation-dissipation theorems. Thus, a non-thermal noise source adds to thermal noise, making biological membranes non-equilibrium, i.e. active membranes. 

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. 

The methods for calculating A/Zexc( ). an equilibrium property of the system, have already been discussed. The dynamic aspects of the permeation process are captured in D (2 ). The fluctuation-dissipation theorem provides the connection between the local diffusion constant and the time autocorrelation function of the random force acting on the solute. 

In this paper we shall develop a new version of Coherent Potential Approximation theory (CPA). We apply a local external field and study the response of the mean field CPA alloy. Because of the fluctuation-dissipation theorem, the response to the external field must be equal to the internal field caused by electrostatic interactions. This new theoretical scheme, avoiding the consideration of specific supercells, will enable us to explore a broad range of fields and clarify certain aspects of the mentioned qV relations. 

Quasilocal soft modes modulate the local dielectric susceptibility of the glass Scik oc aikx and therefore, causes the inelastic light scattering. As a consequence of the fluctuation-dissipation theorem the frequency and temperature dependence of the stokes Raman scattering intensity are determined by... 

Fundamental theory also tells us there is an intimate connection. The fluctuation-dissipation (FD) theorem (7) relates dissipative quantities such as viscosity to the ever present fluctuations in equilibrium systems, such as correlations in local velocities. A significant statement about the viscosity can now be made. The dissipative quantity has the same kind of temperature and pressure discontinuities as does the correlation function. Thus, if we have a first-order diermodynamic transition then we expect the viscosity to display first-order character in its T-P behavior. This is the case. Since we predict an... 

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