Typicality and Notions of Probability in Physics

Meir Hemmo, Orly Shenker

Jeffrey Alan Barrett

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 between the predictions of pure wave mechanics and the standard quantum probabilities.

Lisa Michelle Doumbouya

Physical systems often exhibit stable, repeatable regimes despite being described by equations that allow many possible trajectories. This tension is typically addressed using probabilistic language, with probability treated as a fundamental feature of evolution or as a reflection of stochastic dynamics. In this paper, we argue that probabilistic descriptions instead arise from structural underdetermination in the presence of recurrence and finite resolution. We introduce a coherence-first account in which repeated traversal of structurally admissible pathways reinforces regime stability, leading to effective regime selection without invoking randomness, agency, or additional dynamical mechanisms. Within this framework, probability collapse is not a physical event but a resolution of indistinguishability as recurrence deepens constraint. This perspective completes a structural notion of determinism: outcomes need not be fixed, but admissible regimes are finite, and repeated evolution naturally sharpens their dominance. The resulting picture reconciles deterministic dynamics with probabilistic description while preserving consistency with existing physical formalisms.

A. Spalvieri

The paper works out the canonical probability distribution of the occupancy numbers of a bosonic system and shows that canonical typicality applies to the canonical density operator of the occupancy numbers. The result is that, if, as it is today standard, the canonical system's mixed state is obtained by tracing out the environment from any typical pure state of the universe, then asymptotically the canonical probability distribution of system's occupancy numbers tends in probability to the multinomial distribution. The paper also shows that the currently accepted probability distribution of the occupancy numbers of a system with fixed number of particles is not compatible with the commonly accepted notion of canonical system.

Martin Strauss