Probability and Typicality in Deterministic Physics

Typicality and Notions of Probability in Physics∗

Typicality in Pure Wave Mechanics

Hugh Everett III’s pure wave mechanics is a deterministic physical theory with no probabilities. He nevertheless sought to show how his theory might be understood as making the same statistical predictions as the standard collapse formulation of quantum mechanics. We will consider Everett’s argument for pure wave mechanics, how it depends on the notion of branch typicality, and the relationship...

Typical Worlds

Hugh Everett III presented pure wave mechanics, sometimes referred to as the many-worlds interpretation, as a solution to the quantum measurement problem. While pure wave mechanics is a deterministic physical theory with no probabilities, Everett sought to show how the theory might be understood as making the standard quantum statistical predictions as appearances to observers who were themselv...

Effects of Probability Function on the Performance of Stochastic Programming

Stochastic programming is a valuable optimization tool where used when some or all of the design parameters of an optimization problem are defined by stochastic variables rather than by deterministic quantities. Depending on the nature of equations involved in the problem, a stochastic optimization problem is called a stochastic linear or nonlinear programming problem. In this paper,a stochasti...

Probability as typicality

The concept of typicality refers to properties holding for the “vast majority” of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate viewpoint of the role of probability in classical statistical mechanics, particularly in understanding the micro to macroscopic change of levels