Multiscale nonequilibrium thermodynamics

The review is organized as follows In Section 2 we present the multiscale equilibrium thermodynamics in the setting of contact geometry. The time evolution (multiscale nonequilibrium thermodynamics) representing approach of a mesoscopic level LmeSoi to the level of equilibrium thermodynamics Leth is discussed in Section 3. A generalization in which the level Leth is replaced by another mesoscopic level LmesoZ is considered in Section 4. The notion of multiscale thermodynamics of systems arises in the analysis of this type of time evolution. 

We have just demonstrated that the multiscale nonequilibrium thermodynamics includes the mass action law of chemical kinetics as a particular case. The form (69) of the dissipation potential has been, at least implicitly, introduced already by Marcelin and de Donder (de Donder et al., 1936 Feinberg, 1972 Bykov et al., 1977 Gorban and Karlin, 2003, 2005). In the case when the thermodynamic potential does not have the specific form (66), the fluxes (67) are not exactly the same as the fluxes (64) given by the mass action law. Marcelin and de Donder have suggested that for the modified free energy the fluxes (67) should replace the fluxes given by the mass action law. 

Miroslav Grmela, Multiscale Equilibrium and Nonequilibrium Thermodynamics in Chemical Engineering... 

At least in the traditional domains of chemical engineering and in the traditional core of instructions that chemical engineers receive during their education, fluid mechanics (transport phenomena) has played a key role. Also one of the principal motivations for creating nonequilibrium thermodynamics was an attempt to make fluid mechanics manifestly compatible with equilibrium thermodynamics. Even the noncanonical Hamiltonian structures that play such an important role in the multiscale nonequilibrium thermodyna mics presented in Section 3 have been first discovered... 

Miroslav Grmela, Multiscale Equilibrium and Nonequilibrium Thermodynamics in Chemical Engineering Prasanna K.Jog, Valeriy V. Ginzburg, Rakesh Srivastava, Jeffrey D. Weinhold, Shekhar Jain, and Walter G. Chapman, Application of Mesoscale Field-Based Models to Predict Stability of Particle Dispersions in Polymer Melts... 

Franco has designed this model to coimect within a nonequilibrium thermodynamics framework atomistic phenomena (elementary kinetic processes) with macroscopic electrochemical observables (e.g., I-V curves, EIS, Uceii(t)) with reasonable computational efforts. The model is a transient, multiscale, and multiphysics single electrochemical cell model accounting for the coupling between physical mechanistic descriptions of the phenomena taking place in the different component and material scales. For the case of PEMFCs, the modeling approach can account for detailed descriptions of the electrochemical and transport mechanisms in the electrodes, the membrane, the gas diffusion layers and the channels H2, O2, N2, and vapor... 

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