Nonequilibrium temperature

The concept of a nonequilibrium temperature has stimulated a lot of research in the area of glasses. This line of research has been promoted by Cugliandolo and Kurchan in the study of mean-held models of spin glasses [161, 162] that show violations of the fluctuation-dissipation theorem (FDT) in the NEAS. The main result in the theory is that two-time correlations C t,t ) and responses R t, f ) satisfy a modihed version of the FDT. It is customary to introduce the effective temperature through the fluctuation-dissipation ratio (FDR) [163] dehned as... 

A. Garriga and F. Ritort, Mode dependent nonequilibrium temperatures in aging systems. Phys. Rev. 72, 031505 (2005). 

In the limit l->oo a Boltzmann distribution (with a nonequilibrium temperature) is established almost instantaneously and we can use an approach based on two time scales. Assuming that under these circumstances the solution to the differential equation is a(x) exp (- a(r) ) we get, using the known form of... 

Recently, there has been interest in considering FR for systems coupled to heat reservoirs at different temperatures." The relevant FR for systems modelled using deterministic dynamics was determined and tested numerically in 2001, however interest in heat flow for simple models is important for studies aimed at determining the nonequilibrium temperatures and studying Fourier s Law, and therefore consideration of FR in these systems has received some attention. Gomez-Marin and Sancho and were unable to verify an FR proposed by Jarz5mski and Wojcik, presumably due to neglect of boundary terms in the theoretical analysis that were relevant for their numerical calculations. Visco" has studied the GC FR in a model heat flow problem. 

The nonequilibrium temperature is defined in terms of the kinetic energy per molecule averaged over all species, and this has been supposed equal to the kinetic energy per molecule averaged over a single species. Similarly, multiplying Eq. III.l by... 

Al-Nimr et al. (2000) investigated the effect of the phase-lags in temperature and in heat flux on the nonequilibrium entropy production. As the difference between xj-and Xq increases, the propagation of the entropy production shifts from the diffusive type to the wavy type. For most practical applications involving the dual-phase-lag model, the nonequilibrium temperature may be replaced by the equilibrium temperature. 

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 adiabatic saturation temperature is the steady-state temperature attained when a large amount of water is contacted with the entering gas. The wet bulb temperature is the steady-state nonequilibrium temperature reached when a small amount of water is contacted under adiabatic conditions by a continuous stream of gas. Since the amount of liquid is small, the temperature and humidity of the gas are not changed, contrary to the adiabatic saturation case, where the temperature and humidity of the gas are changed. 

The results obtained from a kinetic description show that the drift vector and the diffusion tensor can be exactly calculated and that they depend on the nonequilibrium state of the gas only through the low order moments of the fluid distribution function. Even more, the fluid state in this case is specified by the nonequilibrium temperature T t) and the irreversible stress tensor F j (f) which is proportional to the velocity gradient Vvq. 

Specifically, the existence of a nonequilibrium temperature in sheared systems lead to a considerable theoretical (Criado-Sancho, 2005 Mauri Leporini, 2006), numerical (Kurchan, 2005 CTHem, 2004 Sarman, 1992) and experimental works with particular emphasis to the nonequUibrium properties of colloidal susp>ensions(Abou Gallet, 2004 Bellon, 2001). These studies are relevant to us because kinetic nonequilibrium temperatures may not follow equipartition and are usually related to the breakdown of the fluctuation-dissipation theorem. 

E. Berlin, O. Dauchot, and M. Droz. Nonequilibrium temperatures in steady-state systems with conserved energy. Physical Review E, 71, 046140, 2005. 

The importance here is to recognise the limitation of the test. In addition to the nonequilibrium temperature of the test and the complex distribution of strain, the curve is measured at 2 rpm, which is an arbitrary time-scale. The material behaviour may be different at other time-scales this situation is exactly like a blind man touching an elephant . In addition, at this time scale the Mooney rheometer is not very sensitive to a small difference between the gum rubbers. Therefore, this method is for the screening and catching only a gross difference among the samples. The Mooney test is performed for the specification in any event, and therefore, it is proposed here to pay attention to the shape of the curves also. 

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