Nonlocal effects in nonisothermal hydrodynamics from the perspective of beyond-equilibrium thermodynamics

Abstract

We examine the origins of nonlocality in a nonisothermal hydrodynamic formulation of a one-component fluid of particles that exhibit long-range correlations, e.g., due to a spherically symmetric, long-range interaction potential. In order to furnish the continuum modeling with physical understanding of the microscopic interactions and dynamics, we make use of systematic coarse graining from the microscopic to the continuum level. We thus arrive at a thermodynamically admissible and closed set of evolution equations for the densities of momentum, mass, and internal energy. From the consideration of an illustrative special case, the following main conclusions emerge. There are two different source terms in the momentum balance. The first is a body force, which in special circumstances can be related to the functional derivative of a nonlocal Helmholtz free energy density with respect to the mass density. The second source term is proportional to the temperature gradient, multiplied by the nonlocal entropy density. These two source terms combine into a pressure gradient only in the absence of long-range effects. In the irreversible contributions to the time evolution, the nonlocal contributions arise since the self-correlations of the stress tensor and heat flux, respectively, are nonlocal as a result of the microscopic nonlocal correlations. Finally, we point out specific points that warrant further discussions.

On the Formulation of Continuum Thermodynamic Models for Solids as General Equations for Non-equilibrium Reversible-Irreversible Coupling

“…This is but one among the myriad possibilities for a generalization of g(r, r ). Even more general non-local effects arise for example in the GENERIC-based modeling of fluids such as colloidal suspensions as based on dynamic density functional theory (Hütter and Brader [26]). There, the non-locality enters both into the static (E and S) and the dynamic (L and M) parts of the model.…”

A Review of the System-Intrinsic Nonequilibrium Thermodynamics in Extended Space (MNEQT) with Applications

“…The requirement of quasi-independence forces the linear size of to be not less than the correlation length as discussed in Section 2 and Section 6.4 ; see also [ 41 ]. Thus, there will be no nonlocal effects ([ 120 , 121 ] (for example)) to consider in the MNEQT as they are subsumed within each subsystem. Each subsystem has its own Hamiltonian containing all the information regarding interactions between its constituent particles and internal variables (see how in Section ) so its microstates will contain the effects of all the interactions in .…”

“…The first one is the extended irreversible thermodynamics (ENEQT) [ 20 ], a well-known CNEQT, which also neglects but treats the corresponding entropy density (ET for the ENEQT)as a state function involving various dissipative fluxes such as the heat flux. As said above, one needs to be careful to incorporate nonlocal effects ([ 120 , 121 ], (for example.)) in the CNEQT.…”

“…To be convinced that the above d i S(t) includes the internally generated irreversibility in Equation ( 121) due to macroheat transfer between Σ 1 (t) and Σ 2 (t), we only have to set d e S(t) = 0 to ensure the isolation of Σ. We reproduce Equation (121) as…”

“…; see Equation (121), which gives rise to the last term above. Thus, setting d e Q l (t) = 0, l = 1, 2 to make Σ isolated, we retrieve d i S(t) in Equation ( 121) as expected.…”