pfinal

Pfinal is a notation used in mathematics, physics, and engineering to denote the final value of a quantity P after a process concludes or at the end of a specified interval. The exact meaning depends on context, but Pfinal consistently signals an end-state value rather than a running or initial quantity.

In probability and statistics, Pfinal often refers to the probability of an event after a process has reached a terminal time or boundary. For example, Pfinal(A) can denote the probability of A after stopping the process at a terminal time, or the probability conditioned on a terminal state. In finite-horizon models, Pfinal is defined as P_N(A) for the final step N, highlighting its dependence on the chosen endpoint.

In dynamical systems and control, Pfinal commonly denotes the steady-state or terminal value: Pfinal = lim_{t→∞} P(t) when this limit exists. It may also represent the value the system approaches under a given policy or input, regardless of the path taken to reach it.

In physics and engineering, when P represents power, Pfinal is the power after the system reaches steady operation; when P represents momentum, it can denote the final momentum after an interaction. The exact interpretation depends on the chosen convention for P in the problem.

Notation and interpretation: Pfinal is not universal and must be defined within each work. Authors specify the quantity P represents, the time horizon or boundary conditions, and how Pfinal is measured or computed. It is often paired with related notations such as Pinitial, Ppeak, or Pf∞ to clarify meaning.