# Tag Info

## Hot answers tagged statistical-mechanics

Accepted

### Why is the Maxwell–Boltzmann formula inapplicable at low temperatures?

Since the explanation was a little more complicated than I initially thought, I figured it would be worth it to combine my comments (and info from Physics SE) into an answer. Quantum particles satisfy ...
• 11.4k

### What exactly is temperature?

Heat is the transfer of energy to or from the body in forms other than matter flow or work (organized energy transfer, such as pushing). Temperature is only a well-defined property for a collective ...
• 1,510

### What exactly is temperature?

Temperature vs kinetic energy [OP:] I've read at many places that temperature is the average kinetic energy of particles present in an object. Temperature has to do with the average kinetic energy ...
• 32.6k

### Details of Boltzmann distribution derivation

What you say is a good idea, but is not quite correct because we must maximize the distribute subject to two constraints. I will reiterate the derivation following along with McQuarrie's Statistical ...
• 12.7k
Accepted

### What is the physical significance of molecular partition function?

The partition function $q=\sum_i\exp(-E_i/k_BT)$ in your question can be regarded as the effective number of levels accessible to the molecule at a given temperature. It also means that in the ...
• 27.6k
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### Entropy change when indistinguishable particles suddenly become distinguishable

Very interesting question. The issue is that your formula for $\ln Q_\mathrm{indis}$ does not hold for $N = 1$. Since the rotational, vibrational and electronic degrees of freedom do not come into ...
• 66.8k
Accepted

### Derivation of mean kinetic energy

A simple validation The result you quoted is the average translational kinetic energy for an ideal gas. First, let's sketch out a rough derivation for the average kinetic energy of a particles of an ...
• 8,335
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### Derive expression for internal energy of mixing and entropy of mixing using statistical thermodynamics

In the solution there are two types of molecules $N_1$ and $N_2$. Assume that they do not interact with one another but simply occupy particular 'lattice' sites by blocking them. The total number ...
• 27.6k
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### What is the classical partition function for a system of anharmonic oscillators?

Here follows a complete mathematical derivation of the expressions for the internal energy and isochoric heat capacity. I am not sure why taking the high-temperature limit is unphysical, but maybe ...
• 4,653
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### Deriving the partition function for a harmonic oscillator

I'm confused why you're interpreting the partition function as a count of states. It can't be a count; it's continuous. The zero point energy doesn't actually matter because you can just shift the ...
• 16.9k
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### How is the volume kept constant in an NVE MD simulation?

The answer to this is linked to how you define the “volume” of your system, and the boundary conditions. The simplest case is simply to consider an isolated systems, like a molecule in gas phase. This ...
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### What is the difference between statistical mechanics and quantum mechanics in terms of accuracy?

Quantum mechanics is about the physics of very small things, molecules and smaller. Classical mechanics is about macroscopic things. Quantum mechanics covers the whole of classical mechanics as well, ...
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### Boltzmann Distribution in Molecular Dynamics Simulation?

Within statistical mechanics (SM) a molecular property $X$ is computed by $$\left<{X}\right>_{SM}=\sum^{states}_i X_i p_i$$where $X_i$ is the value of $X$ for energy state $i$ and $p_i$ is the ...
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### What exactly is temperature?

Temperature is related to kinetic energy, but it can't be simply equated to the average kinetic energy of the system. As I wrote in response to another answer, different systems can have different ...
• 11.6k
Accepted

### Why are MD simulations necessary for obtaining Boltzmann populations?

In principle you can, assuming you are given $V(\{\bf{r_i}\})$ where $\{\bf {r_i} \}$ is the set of variables that define a configuration in the system - this is typically the coordinates of the atoms,...
• 2,530