slowerchanging

Slowerchanging is a term used in discussions of dynamical processes to describe variables or components whose changes occur at rates slower than a chosen reference timescale. The term is relative and its meaning depends on the context and the timescale of interest. It is often applied in modeling to distinguish slow variables from faster ones and to justify simplifications such as quasi-static or adiabatic approximations.

Criteria and measurement: A common criterion is the characteristic timescale τ of a variable, defined as the time required for appreciable change. If τ is much larger than the system’s reference timescale τref, the variable is described as slowerchanging. In practice, one assesses the rate by examining time derivatives, spectral content, or dimensionless ratios that indicate slow dynamics relative to the dominant processes.

Examples: In climate science, ocean temperatures and ice sheet dynamics are typically slowerchanging relative to daily weather patterns. In geology, tectonic movements accumulate across millions of years, slowchanging compared to earthquakes and volcanic eruptions. In cell biology, certain regulatory proteins change concentration over hours or days, slowerchanging than signaling events that occur in seconds.

Relation to modeling: Recognizing slowerchanging components supports methods such as timescale separation, multi-scale modeling, and reduced-order models. The designation is context-dependent and can depend on the chosen threshold for what counts as "slow." Related concepts include slow-fast dynamical systems and quasi-static approximations.