# 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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### Entropy density (entropy per particle)

How I can get this definition for an ideal gas: $s=C v \ln (Pρ^{−\gamma})+ \text{constant}$ ? In this answer it is mentioned that there is a connection with the Sackur-Tetrode relation of the ...
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### What is the link between the meaning of excluded volume and its mathematical derivation?

When we examine real polymer chains we have to consider the interactions between single monomers. Therefore we consider a Lennard-Jones-like potential for bringing two monomers together and calculate ...
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### Is the isothermal isobaric ensemble suitable to describe systems with inhomogeneous pressures (e.g. the atmosphere)

Let's consider a simplified atmosphere which can be described via a hydrostatic equilibrium: https://en.m.wikipedia.org/wiki/Hydrostatic_equilibrium We therefore have a pressure which depends on the ...
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### Maxwell-Boltzmann Statistics is equivalent to a uniform distribution among acessible states?

Both Fermi-Dirac and Bose-Einstein statistics reduce to the Maxwell-Boltzmann statistics in the classical limit of very high temperatures or very low concentration. In the case of very high ...
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### Energy of band of $d$-dimensional semiconductor when voltage $V$ is applied across

Let's say we have a one-dimensional semiconductor and I apply voltage V across it, I want to calculate the energy of a parabolic band, when a source and drain voltage is applied across it. I expect it ...
941 views

### Entropy as a function of temperature: is temperature well defined?

Considering volume and particle number constant, the internal energy $U$ is a function of the entropy: $U=U(S)$. The temperature is then defined as $T=dU(S)/dS$. From here, the temperature is a ...
2k views

### Is thermodynamics only applicable to systems in equilibrium?

So I was going through callen's thermodynamics book and their he says that thermodynamics is only applicable to systems which are in equilibrium and that naturally raised a few questions in my mind ...
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### How do normal modes have group velocity?

Considering phonon dispersion curves in crystals, the group velocity is given by the derivative of frequency with respect to wave vector. But these modes on the dispersion represent normal modes, ...
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### Temperature from the Gibbs entropy

In statistical mechanics, temperature is typically introduced via the Boltzmann entropy as follows. The Boltzmann entropy is $S=k_B \ln W$ where $W$ is the number of microstates. If the system's ...
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### Choosing Zero Chemical Potential

After asking this question: Grand canonical ensemble and chemical potential $\mu=0$, I'm still confused about chemical potential: when have we the freedom to take $\mu=0$? In other words, by ...
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### Why is $\langle{\dot A}A^* \rangle=0$ for dynamical variable $A$?

In page 179 of Hansen and McDonald's book, Theory of Simple Liquids, 3rd edition, 2006, an identity of correlation functions was deduced. Here $C_{AB}(t)$ is the time correlation function between ...
92 views

### Cooling effect caused by evaporation

Evaporation is said to cause cooling effect because it absorbs energy from surroundings to change its phase from that of a liquid to gas. I am in doubt as to why would the surroundings be ready to ...
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### Non-Integer Values in Indistinguishable Particle Combinations Quantum Stat Mech

I am taking a thermodynamics course and we have talked about stat mech and the number of possible combinations of $N$ indistinguishable particles given degeneracy $g$. We stated that for the ...