# Questions tagged [statistical-mechanics]

The study of large, complicated systems by means of statistics and probability theory, in order to extract average properties and to provide a connection between mechanics and thermodynamics.

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### System of particles in classical mechanics and classical statistical mechanics

$\bullet$ Both classical mechanics and classical statistical mechanics can describe the properties of a system of classical particles. $\bullet$ In classical statistical mechanics, we assume that we ...
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### Is evaporation a kind of phase transition?

When liquid is heat up to a critical temperature $T_{c}$, it starts boiling and converting to gas. In statistical mechanics, we learn that it is a phase transition. We studied all the properties near ...
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### Question about notation of a Jimbo's paper

I am reading Jimbo's Introduction to Yang-Baxter Equations. And I am confused by the notation he used in the definition: Here he uses $u\in C$ without previously mentioning what is $C$. I guess ...
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### Interpretation of change in entropy and how to formulate an expression for how much energy required to mix gases.?

From statistical mechanics one cab derive the change of entropy of the mixing of two ideal gases with the result $$\Delta S_\text{mix} = - n R \Sigma_{i} x_i \ln(x_i)$$ where $n$ is the total amount ...
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### Disagreement about solving density of orbital per unit energy of photon gas in a cavity

A conducting 2-D cavity (of area $L^2$) contains a photon gas that satisfies the dispersion relationship: $$\omega^2 =\frac{4\pi^2c^2}{L^2}(n_x^2+n_y^2)$$ and I wish to find the density of the ...
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### Calculating Total energy of 2D Debye monoatomic solid

I am trying to find the total energy of a mono-atomic 2D Debye solid. I started with the density of states: $$D(\omega)=\frac{A\omega}{\pi c^2}$$ where A is the area, $\omega$ the frequency and c ...
34 views

### Graph dimension and phase transitions

In this question I am mainly concerned with phase transitions associated with symmetry breaking. For phase transitions of this type, there are a number of results describing the relationship between ...
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### What happens to topological insulators at finite temperature?

There is a similar question here, but I had a few things I wanted to ask. So basically pretty much all analysis/ theory of topological insulators is for pure wave-functions and conservative ...
53 views

### Thermodynamic description of few-body systems

How large should a system be to become thermal? Thermodynamic description is well-established for systems with large numbers (say, of order of $N_A\sim 10^{23}$) of constituents. Is there a "lower ...
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### Field Theory: Converting $\int_0^{x_0} d^dx$ to $\int_0^{x_0} dr$, where $r=^{\textrm{def}}\|x\|$

For my Statistical Field Theory class (http://www.damtp.cam.ac.uk/user/tong/sft/sft.pdf), the prof converts integrals over each element of a vector $x$ into a single integral over the magnitude of the ...