Nonlocal effects in nonisothermal hydrodynamics from the perspectiveof beyond-equilibrium thermodynamics

摘要

We examine the origins of nonlocality in a nonisothermal hydrodynamic formulation of aone-component fluid of particles that exhibit long-range correlations, e.g., due to a sphericallysymmetric, long-range interaction potential. In order to furnish the continuum modeling withphysical understanding of the microscopic interactions and dynamics, we make use of systematiccoarse graining from the microscopic to the continuum level. We thus arrive at a thermodynamicallyadmissible and closed set of evolution equations for the densities of momentum, mass, and internalenergy. From the consideration of an illustrative special case, the following main conclusionsemerge. 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 Helmholtzfree energy density with respect to the mass density. The second source term is proportional to thetemperature gradient, multiplied by the nonlocal entropy density. These two source terms combineinto a pressure gradient only in the absence of long-range effects. In the irreversible contributionsto the time evolution, the nonlocal contributions arise since the self-correlations of the stress tensorand heat flux, respectively, are nonlocal as a result of the microscopic nonlocal correlations. Finally,we point out specific points that warrant further discussions.