Deterministic system

A system is deterministic when its current state and governing rules uniquely determine its future states. The same state and rules therefore produce the same evolution.

State transition system: A model in which states change according to specified transition rules. Determinism means each state has exactly one permitted successor under the system’s rules.
Stochastic system: A system whose evolution includes probabilistic transitions or random variables. Its rules assign probabilities to possible futures rather than selecting one future uniquely.
Causality: The relation in which one event or condition brings about or influences another. Deterministic laws specify how present conditions causally constrain subsequent states.
Newtonian mechanics: A framework describing motion through Newton’s laws and classical concepts of force, mass, and acceleration. For many well-behaved initial conditions, its equations yield uniquely determined motion.
Initial condition: The values that specify a system’s state at the start of an analysis. A deterministic system’s trajectory is fixed once its initial condition and rules are specified.
Nondeterministic system: A system whose rules permit multiple possible next states from the same state. It differs directly from determinism by allowing several rule-consistent futures.
Initial value problem: A differential equation problem specifying an initial state and seeking a solution evolving from it. Existence and uniqueness results determine whether those data fix exactly one evolution.
Cellular automaton: A discrete model of cells whose states update according to local rules. A fixed update rule makes each configuration determine its next configuration.
State space: The set of all possible states a system can occupy. Each point represents a complete state from which deterministic rules specify subsequent states.
Deterministic chaos: Complex behavior in a deterministic system marked by sensitive dependence on initial conditions. Chaotic systems remain deterministic even when tiny initial differences rapidly separate trajectories.

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