Weakly nonlocal fluid mechanics - the Schrodinger equation

Abstract

A weakly nonlocal extension of ideal fluid dynamics is derived from the Second Law of thermodynamics. It is proved that in the reversible limit the additional pressure term can be derived from a potential. The requirement of the additivity of the specific entropy function determines the quantum potential uniquely. The relation to other known derivations of Schrödinger equation (stochastic, Fisher information, exact uncertainty) is clarified.

major extension and revision

References in corpus (6)

• A Schroedinger link between non-equilibrium thermodynamics and Fisher information
• Uniqueness of conserved currents in quantum mechanics
• Cosmological Perturbation Theory Using the Schrödinger Equation
• Stability of stationary solutions of the Schrodinger-Langevin equation
• Weakly nonlocal continuum physics - the Ginzburg-Landau equation
• Random Dynamics, Entropy Production and Fisher Information

Cited by in corpus (6)

• Holographic fluids: a thermodynamic road to quantum physics
• Unique additive information measures - Boltzmann-Gibbs-Shannon, Fisher and beyond
• Splitting the source term for the Einstein equation to classical and quantum parts
• Thermodynamics of continua: the challenge of universality
• Weakly nonlocal non-equilibrium thermodynamics - variational principles and Second Law
• Irrotational Momentum Fluctuations Conditioning the Quantum Nature of Physical Processes