Holographic fluids: A thermodynamic road to quantum physics

It is well known that the Schrödinger equation can be transformed into the form of a Newton equation, and you get Bohmian dynamics. The Bohmian form can be further transformed and the particle appears as a special, probabilistic fluid. The fluid form is not even an interpretation it is called analogy.

In this talk, I argue that the hydrodynamic form of quantum mechanics is not accidental. I analyse the opposite direction, the specific properties of fluids whose momentum balance can be written as an equation of motion of a particle, and the conditions under which this equation of motion can be expressed as an evolution equation of a complex scalar field. It turns out that the second law of thermodynamics plays a crucial role in this respect, determining conditions even for the marginal case of perfect, non-dissipative fluid medium. The fluid that can be represented as a particle is called holographic. The holographic property follows from the entropy inequality in the limit of perfect fluids. The analysis requires constructive methods of modern nonequilibrium thermodynamics. The methodology is universal. It is independent of the structure and composition of the material, be it a field or particle ensemble. In the talk, I will briefly discuss further implications, applications and shortcomings of the methodology, the role of the second law in quantum foundations. The bridge between the field and particle representations of a physical system is holography, and the key to holography is the second law of thermodynamics.