Timenonlocal

Timenonlocal, or time nonlocal, is a term used to describe situations in which the evolution of a system depends on its state at distant points along the time axis, rather than solely on its instantaneous state. This concept is distinct from spatial nonlocality, though both involve correlations that cannot be fully explained by strictly local models.

In physics, time nonlocality often arises in systems with memory or non-Markovian dynamics. For such systems, the present state depends on a history of past states, frequently represented by integral equations with a memory kernel or by fractional time derivatives. This leads to temporal correlations that extend beyond immediate cause-and-effect assumptions. Time nonlocality also appears in open quantum systems where interactions with an environment create lasting memory effects, and in certain theoretical formulations where advanced, rather than purely retarded, temporal terms contribute to dynamics.

In quantum mechanics, temporal correlations are studied through tests of macrorealism, such as the Leggett-Garg inequality. Violations of these inequalities suggest a form of temporal nonlocality, indicating that classical ideas of a system possessing definite properties at all times cannot fully describe observed correlations. This line of inquiry helps distinguish quantum coherence in time from classical temporal behavior and is discussed in both foundational and applied contexts, including quantum information and control theory.

While time nonlocality challenges intuitive notions of causality, it does not imply superluminal signaling or violation of relativistic causality within standard frameworks. It is typically understood as a feature of correlations over time rather than instantaneous spatial influence.

See also: nonlocality, Leggett-Garg inequality, non-Markovian dynamics, memory effects, fractional calculus.