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In statistical physics , the missing information of a system is the information that is needed to describe the state in which a system is. It is the weighted sum of the logarithms of the state probabilities
where which are the probabilities of the states of the system.
As information entropy , the missing information is referred to, which describes in what state a randomly chosen example of a representative to the ensemble is located.
If one sets , then the information content results from the information theory in the unit Shannon . In statistical physics, the Boltzmann constant is used as a proportionality factor because the information entropy of an ensemble then corresponds to the thermodynamic entropy .
The vestibular system is in this usage the system with the maximum lack of information.
In the micro-canonical ensemble, all states are represented equally frequently. Is there for the macroscopic state in which z. If, for example, the energy, the number of particles and the volume are a number of microscopic states, the energy levels are consequently represented by the probabilities .
W. Dieterich, Oliver Schlotterer: Statistical Mechanics. (PDF; 2.4 MB) Lecture in WS 2004/5. Physics Department, University of Konstanz, February 2009, pp. 57–61 , accessed on January 21, 2012 .
Horst Völz : Description of the world. Space, time, temperature and information - aspects, positions, debates. Shaker Verlag, Aachen 2018, ISBN 978-3-8440-6323-3 .