### Abstract

We derive the fluctuating hydrodynamic equation for the number and momentum densities exactly from the underdamped Langevin equation. This derivation is an extension of the Kawasaki-Dean formula in the underdamped case. The steady-state probability distribution of the number and momentum densities field can be expressed by the kinetic and potential energies. In the massless limit, the obtained fluctuating hydrodynamic equation reduces to the Kawasaki-Dean equation. Moreover, the derived equation corresponds to the field equation derived from the canonical equation when the friction coefficient is zero.

Original language | English |
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Article number | 065001 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2009 Apr 20 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

Nakamura, T., & Yoshimori, A. (2009). Derivation of the nonlinear fluctuating hydrodynamic equation from the underdamped Langevin equation.

*Journal of Physics A: Mathematical and Theoretical*,*42*(6), [065001]. https://doi.org/10.1088/1751-8113/42/6/065001