On Entropy Production in the Madelung Fluid and the Role of Bohm’s Potential in Classical Diffusion

@article{Heifetz2015OnEP,
  title={On Entropy Production in the Madelung Fluid and the Role of Bohm’s Potential in Classical Diffusion},
  author={Eyal Heifetz and Roumen Tsekov and Eliahu Cohen and Zohar Nussinov},
  journal={Foundations of Physics},
  year={2015},
  volume={46},
  pages={815-824}
}
The Madelung equations map the non-relativistic time-dependent Schrödinger equation into hydrodynamic equations of a virtual fluid. While the von Neumann entropy remains constant, we demonstrate that an increase of the Shannon entropy, associated with this Madelung fluid, is proportional to the expectation value of its velocity divergence. Hence, the Shannon entropy may grow (or decrease) due to an expansion (or compression) of the Madelung fluid. These effects result from the interference… 
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References

SHOWING 1-10 OF 22 REFERENCES
Toward a Thermo-hydrodynamic Like Description of Schrödinger Equation via the Madelung Formulation and Fisher Information
We revisit the analogy suggested by Madelung between a non-relativistic time-dependent quantum particle, to a fluid system which is pseudo-barotropic, irrotational and inviscid. We first discuss the
Dissipation caused by a vorticity field and generation of singularities in Madelung fluid
We consider a generalization of Madelung fluid equations, which was derived in the 1980s by means of a pathwise stochastic calculus of variations with the classical action functional. At variance
On the hydrodynamical model of the quantum mechanics
SummaryA new hydrodynamicla model for the Schrödinger equation is discussed. The new model differs from that ofMadelung by the existence of turbulence. It follows directly from the ordinary
Differential Entropy and Dynamics of Uncertainty
We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The
On the Role of Spin in Quantum Mechanics
From the invariance properties of the Schrödinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an “external” motion, which can be
Bohmian mechanics versus Madelung quantum hydrodynamics
It is shown that the Bohmian mechanics and the Madelung quantum hydrodynamics are different theories and the latter is a better ontological interpretation of quantum mechanics. A new stochastic
Fluid Mechanics
Ludwig Krinner (Dated: November 5th 2012) Abstract This is a script made with the help of Landau Lifshitz, Book VI [1] on fluid mechanics, that gives a short introduction to basic fluid mechanics.
Interpretation of the hydrodynamical formalism of quantum mechanics
The hydrodynamical formalism for the quantum theory of a nonrelativistic particle is considered, together with a reformulation of it which makes use of the methods of kinetic theory and is based on
Quantum Brownian motion and classical diffusion
Abstract A new approach to the description of quantum Brownian motion, based on the extension of the equation governing the probability density evolution, is developed. It takes into account both the
Microscopic diagonal entropy and its connection to basic thermodynamic relations
The author acknowledges helpful discussions with R. Barankov on earlier stages of this work. The author also thanks C. Gogolin for sharing the proof of Eq. (24) and for many valuable comments. It is
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