aikaderivaationsa

Aikaderivaationsa is a theoretical construct used to describe the rate of change of a quantity with respect to an internal time variable, rather than external laboratory time. The term combines Finnish roots aika (time) and derivaation (derivative). In discussions of non-stationary or clock-dependent systems, aikaderivaationsa denotes the derivative dQ/dτ, where τ is a system-defined clock parameter.

The concept is not part of standard nomenclature in physics or mathematics but appears in speculative or interdisciplinary literature on dynamic time scales and internal clocks.

Suppose Q(t) is a state variable. Define an internal clock τ(t) by dτ/dt = h(Q,t) with h>0. Then aikaderivaationsa is dQ/dτ = (dQ/dt)/(dτ/dt) = (dQ/dt)/h(Q,t). For a vector Q, the Jacobian relative to τ is J_τ = J_t / h.

It measures how the state evolves when the flow of time is reparameterized by h. In models with resource constraints or circadian modulation, aikaderivaationsa can reveal intrinsic dynamics obscured by external time. Example: in a population model under changing resource availability, the internal-time derivative highlights growth phases more clearly than the external-time derivative.

The choice of h is not unique; aikaderivaationsa is not invariant under general reparameterizations. It relates to the concept of proper time or time reparametrization in relativity, and to time-scale calculus in applied mathematics.

See also: Time derivative, Internal time, Time reparametrization. This entry describes a speculative construct and is not part of established scientific nomenclature.