Evershift

Evershift is a term used in discussions of reversible dynamics and phase progression to describe a state transition that is invertible and that, with each application, advances a global phase parameter by a fixed amount, modulo a defined period.

In formal terms, let X be a state space, S: X → X an invertible evolution operator, and f: X → R (or Z) a phase function. An evershift with step size c and period T satisfies f(S(x)) = f(x) + c (mod T) for all x in X. Repeated application yields f(S^n(x)) = f(x) + n c (mod T). The operator S preserves the structure of X and is reversible, so S^{-1} exists and undoes each step. The combination (S, f) provides a way to track a cyclic phase progression that can be independently reset or reversed.

Origins and usage of the term are informal; it has appeared in speculative fiction, online wikis, and discussions on reversible computing and time-symmetric models. It is typically used to illustrate ideas of phase cycling, information preservation, and time-reversal symmetry rather than as a formally established technical standard.

Examples and applications include reversible programming, where an evershift–like construct can encode a clock that advances computation while preserving all intermediate states. In theoretical physics, it serves as a toy model for phase evolution under time-reversal symmetry. In simulations, an evershift may describe a rotating phase variable that returns to its starting point after a fixed number of steps.

See also: Reversible computing, Time symmetry, Phase shift, Cyclic group.