Brillouin's negentropy in an Einstein solid

[Ted Ali]

Hello!
I would like to apply Brillouin's negentropy principle to an isolated Einstein solid, with a decreasing number of oscillators. We assume that the number of oscillators are initially N and the energy quanta (q the number) remain constant.
Firstly, I would like to know if this principle is applicable in this case.
Secondly, I would like to calculate the formula for Information I, when N decreases by one (1) unit.
My calculations:
$$ \Omega_N = \frac{(N - 1 + q)!}{(N - 1)!q!} $$ So, $I =k\ln{\frac{\Omega_N}{\Omega_{N-1}}} =k\ln \left( \frac{N - 1 + q}{N - 1} \right).$

Please let me know if I am correct.
Thank you in advance,
Ted.

 

[eljose79]

Hello Ted,

Thank you for your interest in applying Brillouin's negentropy principle to an isolated Einstein solid. The principle is indeed applicable in this case, as it is a general thermodynamic principle that can be applied to any system.

Your calculation for the formula of information I when N decreases by one unit is correct. The formula for information in this case is:

$$ I = k\ln\left(\frac{N+q}{N}\right) $$

This formula shows that as the number of oscillators decreases, the information decreases as well. This is because the system becomes less complex and has fewer possible states.

I would also like to mention that the concept of negentropy, or negative entropy, is often used to describe the organization or order in a system. In the case of an isolated Einstein solid, as the number of oscillators decreases, the system becomes less organized and therefore has a decrease in negentropy.

I hope this helps and feel free to ask any further questions. Best of luck with your research.