Principle of maximum caliber and quantum physics

Abstract

MaxCal is a variational principle that can be used to infer distributions of paths in the phase space of dynamical systems. It has been successfully applied to different areas of classical physics, in particular statistical mechanics in and out of equilibrium. In this work, guided by the analogy of the formalism of MaxCal with that of the path integral formulation of quantum mechanics, we explore the extension of its applications to the realm of quantum physics, and show how the Lagrangians of both relativistic and nonrelativistic quantum fields can be built from MaxCal, with a suitable set of constraints. Related, the details of the constraints allow us to reinterpret the concept of inertia.

Visualizing Quantum Circuit Probability: Estimating Quantum State Complexity for Quantum Program Synthesis

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Solving Equations of Motion by Using Monte Carlo Metropolis: Novel Method Via Random Paths Sampling and the Maximum Caliber Principle

“…This technique is based on sampling a statistical ensemble of paths defined as having the maximum path entropy (also known as the caliber) available under imposed time-dependent constraints. In Section 2 , we introduce this approach, which is known as the maximum caliber principle (MaxCal) [ 1 ], a generalization of Jaynes’ principle of maximum entropy [ 2 , 3 , 4 ].…”