Thermodynamics mesoscopic

Another approach towards a thermodynamics of steady-state systems is presented by Santamaria-Holek et al.193 In this formulation a local thermodynamic equilibrium is assumed to exist. The probability density and associated conjugate chemical potential are interpreted as mesoscopic thermodynamic variables from which the Fokker-Planck equation is derived. Nonequilibrium equations of state are derived for a gas of shearing Brownian particles in both dilute and dense states. It is found that for low shear rates the first normal stress difference is quadratic in strain rate and the viscosity is given as a simple power law in the strain rate, in contrast to standard mode-coupling theory predictions (see Section 6.3). 

Two major features must be introduced into the standard thermodynamic framework in order to apply thermodynamics at meso-scales fluctuations and local (coordinate-dependent) properties. Thermodynamics of equilibrium fluctuations is a well developed science and we will briefly address this topic in this section. Incorporating the local inhomogeneities is another task of mesoscopic thermodynamics. In this section we introduce a phenomenological approach, which is restricted to fluids with smoothly varying properties, known as local or quasi thermodynamics, and which dates back to van der Waals. ... 

The simplest way to connect the mesoscopic susceptibility with other thermodynamic properties and introduce smooth heterogeneities into mesoscopic thermodynamics is to consider a local (coordinate-dependent) thermodynamic... 

Santamaria Holek, I., e. a. (2005). Mesoscopic thermodynamics of stationary non-equilibrium... 

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