Physical information

In statistical physics the missing information of a system is the information that is needed to find out what state a system is located. It is the weighted sum of the logarithms of the state probabilities

Which are the probabilities of the n states of the system.

As information entropy S is the lack of information is called to find out in what condition is a randomly chosen example representative of an ensemble.

Substituting, we obtain the information content from information theory in the unit Shannon. In statistical physics is used, but k is the Boltzmann constant, because then matches the information entropy of an ensemble with the thermodynamic entropy.

The vestibular system is in this usage, the system with the maximum of lack of information.

Microcanonical Ensemble

In the microcanonical ensemble, all states are equally represented. Exist for macroscopic state in which, for example, E is the energy, N is the number of particles, and V is the volume, a number of microscopic conditions, so, consequently, the energy levels are represented by the probabilities.

The information entropy is then

Or for a specific energy

Canonical Ensemble

The probabilities of various energies and the information entropy for the canonical ensemble are of

Where F is the free energy and U is the internal energy.

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