What is spectral entropy?
Spectral Entropy describes the complexity of a system. It is defined as follows:


Calculate the spectrum $X(\omega_i)$ of your signal.
Calculate the Power Spectral Density of your signal via squaring its amplitude and normalizing by the number of bins.


$$P(\omega_i)=\dfrac{1}{N}\left|X(\omega_i) \right|^2 $$


Normalize the calculated PSD so that it can be viewed as a Probability Density Function (integral is equal to 1).


$$p_i=\dfrac{P(\omega_i)}{\sum_iP(\omega_i)} $$


The Power Spectral entropy can be now calculated using a standard formula for an entropy calculation.


$$PSE = -\sum_{i=1}^np_i\ln p_i $$

In case of boosting of your noise signal, without performing any other processing, the Entropy will change. I guess there is no other way around that.