Differential entropy of Gaussian R.V. is $\log_2(\sigma \sqrt{2\pi e})$. This is dependent on $\sigma$, which is the standard deviation.

If we normalize the random variable so that it has unit variance its differential entropy drops. To me this is counter-intuitive because Kolmogorov complexity of normalizing constant should be very small compared to the reduction in entropy. One can simply devise an encoder decoder which divides/multiples with the normalizing constant to recover any dataset generated by this random variable.

Probably my understanding is off. Could you please point out my flaw?

Thank you

Differential entropy of Gaussian R.V. is $\log_2(\sigma \sqrt{2\pi e})$. This is dependent on $\sigma$, which is the standard deviation.

If we normalize the random variable so that it has unit variance its differential entropy drops. To me this is counter-intuitive because Kolmogorov complexity of normalizing constant should be very small compared to the reduction in entropy. One can simply devise an encoder decoder which divides/multiples with the normalizing constant to recover any dataset generated by this random variable.

Probably my understanding is off. Could you please point out my flaw?

Differential entropy of Gaussian R.V. is $ln(\sigma(2\pi e)^.5)$. This is dependent on $\sigma$, which is the standard deviation.

If we normalize the random variable so that it has unit variance its differential entropy drops. To me this is counter-intuitive because Kolmogorov complexity of normalizing constant should be very small compared to the reduction in entropy. One can simply devise an encoder decoder which divides/multiples with the normalizing constant to recover any dataset generated by this random variable.

Probably my understanding is off. Could you please point out my flaw?

Thank you

Differential entropy of Gaussian R.V. is $\log_2(\sigma \sqrt{2\pi e})$. This is dependent on $\sigma$, which is the standard deviation.

If we normalize the random variable so that it has unit variance its differential entropy drops. To me this is counter-intuitive because Kolmogorov complexity of normalizing constant should be very small compared to the reduction in entropy. One can simply devise an encoder decoder which divides/multiples with the normalizing constant to recover any dataset generated by this random variable.

Probably my understanding is off. Could you please point out my flaw?

Thank you