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Area of Science:

  • Computational physics
  • Statistical mechanics
  • Mesoscopic physics

Background:

  • Coarse-grained models simplify microscopic systems.
  • Mesoscopic momentum definitions are crucial for these models.
  • Uniqueness of momentum definitions at coarse-grained scales is often assumed.

Purpose of the Study:

  • To investigate the uniqueness of momentum definitions in coarse-grained methods.
  • To compare common momentum definitions with a fundamental one.
  • To analyze discrepancies in fluctuating properties.

Main Methods:

  • Analysis of coarse-grained methods, including lattice gas and lattice Boltzmann.
  • Derivation of analytical representations for momentum measure distributions.
  • Comparison of different momentum definitions.

Main Results:

  • Common momentum definitions in lattice gas and lattice Boltzmann methods show discrepancies with fundamental definitions.
  • Disagreement persists even for large wavelengths in lattice gases.
  • Analytical representations reveal differences in momentum measure distributions for short times.

Conclusions:

  • The choice of momentum definition in coarse-grained methods impacts results.
  • Fluctuating properties are key indicators of these discrepancies.
  • Further investigation into fundamental momentum definitions is warranted for accurate mesoscopic modeling.