# Tagged Questions

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### Does the canonical partition function count microstates?

The microcanonical partition function is the density of states. The canonical one, from a dimensional point of view, is still a number of states, but does it actually count microstates? I tried ...
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### How exact is the analogy between statistical mechanics and quantum field theory?

Famously, the path integral of quantum field theory is related to the partition function of statistical mechanics via a Wick rotation and there is therefore a formal analogy between the two. I have a ...
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### Partition Function And Macroscopic Properties

In renormalization group transformations, partition function is fixed. My question is which thermodynamic properties are fixed in a renormalization group transformation.
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### What is the physical meaning of a Partition Function in Statistical physics?

In many places in statistical physics we assume the partition function. To me the explanations after partition functions are most of the times clear but always wonder why a partition function and what ...
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### Is there a local canonical ensemble partition function for a Bose-Einstein gas?

The grand canonical partition function for a Bose-Einstein gas is $$Z_{\text{grand bos}} = \exp \left( \sum_{j=0}^{\infty} -\ln \left( 1-e^{\beta(\mu-\epsilon_j)} \right)g_j \right)$$ where $\beta$ ...
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### Why is the partition function divided by $(h^{3N} N!)$?

When computing partition functions for classical systems with $N$ particles with a given Hamiltonian $H$ I've seen some places writing it as $$Z = \dfrac{1}{h^{3N} N!}\int e^{-\beta H(p,q)}dpdq$$ ...
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### Multiplicity vs Partition function

I'm a little confused between all the different notations for the multiplicity and partition function. They're not the same thing, are they? I know that entropy can be expressed as $S = k \ln\Omega$...
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### potential energy of a segment of an ideal chain under external force

I want to construct the partition function of an ideal chain under applied external force. Let's say we apply force to both ends (with opposite sign) acting in z-direction and a segment of the ideal ...
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### A trace formula of two noncommutative operators

In many cases of quantum many-body problems, the Hamiltonian $H$ can always be divided into two parts, i.e. $H_0$ and $H'$. In this occasion, one can systemically calculate the partition function ...
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### Partition function is simply temperature if possible sub system energy is continuous?

Partition function is $$Z=\sum_j\exp\left(-\frac{\epsilon_j}{kT}\right)$$ a sum over all possible energy levels $\epsilon_1,\epsilon_2, ..., \epsilon_M$. There must be a finite number of choices ...
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### Einstein model for thermal capacity of solids and indistinguishability of the oscillators

Albert Einstein's theory of thermal capacity of a solids makes the assumption that a crystal is made up from oscillators which of course oscillate, in all three directions. Thus, for N atoms of the ...
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### Difference in partition function of classical and quantum Ideal gas

First, I have read this question:What is meant by the term "single particle state" There is an analysis going on in my book (Mandle F. Statistical Physics) that has brought me in a ...
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### Is there a way to obtain the classical partition function from the quantum partition function in the limit $h \rightarrow 0$?

One would like to motivate the classical partition function in the following way: in the limit that the spacing between the energies (generally on the order of $h$) becomes small relative to the ...
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### What is the definition of 'relative population' in context of partition function?

In statistical mechanics, what is the definition (or mathematical definition) when authors refer to relative population in the case of a classical particle system?
### is it necessarily true that the partition function $Z$ (with degeneracies) $=1$?
The partition function with degnerate energies is $$\text{Z}=\sum _ig_ie^{{-E_i}/{k_BT}}.$$ Because the partition function Z is defined as the normalisation constant, does Z always = 1?
The Single particle partition function is defined mathematically as $$\text{Z=\sum }g_ie^{\left(\frac{-E_i}{K_BT}\right)}$$ But what is the physical interpretation of the partition function and it'...