Abstract
The hydrodynamic level of description is an extension of the thermodynamic level that takes into account the dependence of the extensive variables on spatial coordinates. Even an ensemble in which the systems are spatially uniform on the average involves fluctuations that differ from one position to another. Consider, for example, the particle mass density, ρ(r, t), in a simple fluid like water. In an equilibrium ensemble the average density, ρe, will be constant in the absence of an external field. Because of the molecular nature of water it is clear that at a given time t and position r different members of the ensemble will possess different values of the number density. We have already encountered this at the Boltzmann level of description in Sections 3.2 and 3.3. There it was necessary to keep track of the number of particles with a given range of positions and momenta. The hydrodynamic level is intermediate between the Boltzmann and thermodynamic levels and adds the momentum to the basic extensive thermodynamic variables. At the hydrodynamic level one has a closed description of the spatial dependence of the densities of extensive variables throughout a system.
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Keizer, J. (1987). The Hydrodynamic Level of Description. In: Statistical Thermodynamics of Nonequilibrium Processes. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1054-2_6
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DOI: https://doi.org/10.1007/978-1-4612-1054-2_6
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