Recurrencefree

Recurrencefree is a term used to describe a process, sequence, or system that does not exhibit recurrence—the return to previously visited states or values. While the exact interpretation depends on context, it generally signals the absence of repetition over time.

In mathematics, a sequence is recurrence-free if all its terms are distinct. Equivalently, no term equals a previous term. An example is the natural-number sequence a_n = n, which never repeats. In contrast, many commonly studied sequences, such as 1, 1, 2, 3, 5, 8, are not recurrence-free because they contain repeated values or patterns.

In dynamical systems, recurrence typically means that trajectories revisit neighborhoods of initial states under iteration. A recurrencefree system would fail to revisit prior states within its phase space, a property more likely in non-compact, escaping, or dissipative dynamics. In many bounded systems, recurrence is a common phenomenon due to constraints on the state space.

In computer science and machine learning, recurrencefree is used to describe architectures or models that do not use recurrent connections, such as standard feedforward networks. It can also describe data-processing schemes designed to avoid reprocessing the same state, though some modern models incorporate memory in alternative forms.

The term is relatively informal, and its precise meaning is defined by its user. As such, recurrencefree serves as a convenient way to discuss ideas related to repetition, memory, and state visitation across disciplines. Related concepts include recurrence relations, aperiodicity, non-recurrence, and non-revisiting sequences.