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

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.