forcning

Forcing, commonly spelled forcing but occasionally seen as forcning, is the external influence that acts on a system, altering its state, trajectory, or equilibrium. The term appears across disciplines, and its precise meaning depends on context.

In physics and engineering, forcing refers to an external input that drives a dynamic system. For example, a differential equation may include a forcing term F(t) that represents an external force or input, distinct from the system’s internal dynamics. In control theory, forcing functions specify external signals used to steer a system’s behavior.

In climate science, the concept often appears as radiative forcing. Radiative forcing measures the change in the energy balance at the top of the atmosphere due to external agents such as greenhouse gases, aerosols, or volcanic eruptions. Positive forcing tends to warm the climate, while negative forcing tends to cool it. Radiative forcing is a central metric for comparing the potential climate impact of different drivers.

In mathematics, forcing is a technique developed to prove statements are independent of established axioms, notably by Paul Cohen in the 1960s. Forcing involves extending a model of set theory by adding a generic filter relative to a partially ordered set, creating a larger model in which certain propositions can be true or false as intended.

In other contexts, forcing can describe periodic or seasonal drivers in biology and ecology, where external factors such as temperature or daylight act as forcing terms that modulate population cycles or physiological processes.