Hot Fluids and Nonlinear Quantum Mechanics

Abstract: It is shown that a hot relativistic fluid could be viewed as a collection of self-interacting quantum objects. They obey a nonlinear equation which is a modification of the quantum equation obeyed by elementary constituents of the fluid. A uniform phenomenological prescription, to affect the quantum transition from a corresponding classical system, is invoked to derive the nonlinear Schr\"odinger, Klein-Gordon, and Pauli-Schr\"odinger equations. It is expected that the created nonlinear quantum mechanics would advance, in a fundamental way, both the conceptual understanding and computational abilities, particularly, in the field of extremely high energy-density physics.