Unified Description of Classical and Quantum Behaviours in a Variational Principle

Abstract

We give a pedagogical introduction of the stochastic variational method and show that this generalized variational principle describes classical and quantum mechanics in a unified way.

arXiv comment10 pages, no figure, proceedings of DICE 2014, references and discussions were added, errors were corrected

References in corpus (5)

• Entropic Dynamics, Time and Quantum Theory
• Navier-Stokes, Gross-Pitaevskii and Generalized Diffusion Equations using Stochastic Variational Method
• Navier-Stokes Equation by Stochastic Variational Method
• Thermodynamic Gravity and the Schrodinger Equation
• Equivalence of the Klein-Gordon random field and the complex Klein-Gordon quantum field

Cited by in corpus (7)

• Generalization of Uncertainty Relation for Quantum and Stochastic Systems
• Novel Effect Induced by Spacetime Curvature in Quantum Hydrodynamics
• Uncertainty Relations in Hydrodynamics
• Perturbative Expansion of Irreversible Work in Fokker-Planck Equation a la Quantum Mechanics
• Uncertainty relation for angle from a quantum-hydrodynamical perspective
• Variational formulation of compressible hydrodynamics in curved spacetime and symmetry of stress tensor
• Viscous control of minimum uncertainty state in hydrodynamics