Nonuniqueness of fluctuating momentum in coarse-grained systems

Coarse-grained descriptions of microscopic systems often require a mesoscopic definition of momentum. The question arises as to the uniqueness of such a momentum definition at a particular coarse-graining scale. We show here that particularly the fluctuating properties of common definitions of momentum in coarse-grained methods like lattice gas and lattice Boltzmann do not agree with a fundamental definition of momentum. In the case of lattice gases, the definition of momentum will even disagree in the limit of large wavelength. For short times we derive analytical representations for the distribution of different momentum measures and thereby give a full account of these differences.

Automated summary

In this study, the authors discuss the issue of momentum definition in coarse-grained descriptions of microscopic systems, particularly the discrepancy between the fluctuating properties of common momentum definitions in lattice gas and lattice Boltzmann methods and a fundamental definition of momentum. Analytical representations for the distribution of different momentum measures are derived, providing a comprehensive account of these differences.