deterministically

Deterministically is an adverb describing actions performed in a way that every outcome is fixed by the initial conditions and the rules governing the system. When something is deterministic, repeating it with the same inputs and conditions yields the same result. The term is common in mathematics, computer science, physics, and philosophy.

In computing, a deterministic algorithm, function, or process is one that, given the same input, always produces the same output and follows a predictable path of execution. Deterministic models contrast with probabilistic or non-deterministic ones, where randomness or multiple possible paths can occur. Pseudorandom number generators are deterministic in the sense that the same seed yields the same sequence of numbers. Deterministically bounded systems are important for reproducibility and verification.

In mathematics and physics, determinism refers to the idea that all events are determined by prior states and laws. In classical physics and many mathematical models, processes are modeled deterministically. In quantum mechanics, some interpretations posit fundamental indeterminacy, which challenges naive determinism but is nuanced.

Etymology: From Latin determinare, meaning to set bounds or to determine. The suffix -ly forms adverbs in English.