In my physical model I have two variables $x_1$ and $x_2$. I also have a non-linear monotonic function $y=f(x)$ which gives reasonable result only when it is evaluated for the sum of two inputs $x_1 + x_2$.
To clarify, with two inputs $x_1$ and $x_2$ available I can evaluate said function and obtain
- $y_1=f(x_1)$ - result is physically meaningless,
- $y_2=f(x_2)$ - result is physically meaningless,
- $y_{1+2}=f(x_1 + x_2)$ - result is physically sound.
However, after evaluation of $y_{1+2}$ I need somehow to decompose $y_{1+2}$ into $y_{1+2} = y_1^* + y_2^*$, which are physical quantaties, for further calculations.
Obviously, $y_{1+2}\neq y_1 + y_2$, but can be anything said at least about the ratio of the outputs $y_1^*$ and $y_2^*$, e.g.:
- $\frac{y_2^*}{y_1^*} = \frac{x_2}{x_1} $ ,
- $\frac{y_2^*}{y_1^*} = \frac{y_2}{y_1} $ ?