Preprint.

**ISSN/ISBN:** Not available at this time.
**DOI:** Not available at this time.

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**Abstract:** The canonical partition function, which represents exponential energy decay between the canonical ensemble states, is a cornerstone of the mechanical statistics. All the thermodynamic state-functions derived from it. The canonical partition function yields correctly many statistical phenomena but it fails to explain the long-tail distribution. The canonical ensemble conserves material and volume, and it has a constant temperature – but it does exchange energy with an external bath. Hereafter it is claimed that this model is incorrect. Here we claim that the canonical ensemble is the quantum limit approximation of a microcanonical ensemble that conserves material, volume, and energy. Since it conserves energy, its temperature is constant. In addition, according to the second law, in equilibrium, all its states and all its microstates have equal energy. The partition function of this microcanonical ensemble converges to the canonical partition function in the quantum limit, and to the power-law energy distribution in the classical limit. Therefore, the canonical ensemble is a private case of the microcanonical ensemble.

**Bibtex:**

```
@misc{,
author = {Oded Kafri},
title = {
year = {2020},
url = {https://www.researchgate.net/profile/Oded_Kafri/publication/339166312_Microcanonical_Partition_Function/links/5e4262d2299bf1cdb91f7b71/Microcanonical-Partition-Function.pdf},
}
```

**Reference Type:** Preprint

**Subject Area(s):** Physics, Probability Theory