Equations of one-dimensional hydrodynamics with quantum thermal fluctuations taken into account

TL;DR

This paper develops a generalized hydrodynamic model incorporating quantum and thermal fluctuations, extending Nelson's stochastic mechanics to describe nearly perfect fluid states.

Contribution

It introduces a new set of equations that include diffusion velocity and diffusion pressure energy, advancing the modeling of quantum thermal effects in hydrodynamics.

Findings

Derived equations extend Nelson's stochastic mechanics.

Applicable to modeling nearly perfect fluid states.

Incorporates quantum and thermal effects into hydrodynamic equations.

Abstract

We propose a generalization of equations of quantum mechanics in the hydrodynamic form by introducing the terms taking into account the diffusion velocity at zero and finite temperatures and the density energy of diffusion pressure of the thermal vacuum into the Lagrangian density. Based on this, for a model of one-dimensional hydrodynamics, we construct a system of equations that are similar to the Euler equations but taking quantum and thermal effects into account. They are a generalization of equations of Nelson's stochastic mechanics and can be used to describe a new matter state, namely, nearly perfect fluidity.