# 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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### How Can Energy of the Canonical Ensemble Vary?

Canonical ensemble is an statistical ensemble which is applicable for the closed system in contact with the reservoir at constant temperature $T$. Canonical ensemble is characterized by the three ...
1 vote
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### Blackbody radiation as a stochastic process

Can one treat the blackbody radiation as a stochastic process of photon emission? If so, what stochastic process is it (perhaps a Poisson process?)?
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### Doubt with partial pressures

I have a conceptual doubt about partial pressures. Suppose you have a closed system composed of a gas mixture, say Argon and Helium. If they behave according to Ideal Gas Law, then the molar fraction ...
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### Derivation of the Canonical Ensemble

One of the common derivations of the canonical ensemble goes as follows: Assume there is a system in the contact with heat reservoir which together form an isolated system. Heat can be exchanged ...
1 vote
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### When can we guarantee a closed form of statistical mechanical equations?

Consider the equation of state: $$P = \rho k_BT$$ where $P$ is pressure, $\rho$ is number density, $k_B$ is Boltzmann constant and $T$ is temperature. All variables are intensive thermodynamic ...
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### Fermi energy at zero temprature

If I have a beaker that is at zero temperature in thermal equilibrium with its surrounding. If I start filling fermions (say electrons) in it, then according to the Fermi-Dirac statistics, the energy ...
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### I need MATLAB or Mathematica code to solve this integral over limit 0- λ [migrated]

I want the code to integrate equation(1) or (2) over the limits using mathematical or mathlab to get equation (3) as the answer of $Z$ vibrational partition function, giving the following additional ...
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### Expanding ensemble averages

I am reading Statistical Physics of Particles by Kardar. I am struggling with problem 12d, in chapter 2, about semi-flexible polymers in two dimensions. The problem is as follows: Configurations of a ...
1 vote
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### Formulation of entropy distance from equilibrium for fluctuations of the extensive parameters

I am looking for a valid definition/formulation of the distance from equilibrium entropy $\Delta S$, with the request that: $$0 \geq \Delta S \hspace{1cm} (1)$$ The fluctuations in the extensive ...
108 views

### What is the temperature of an atomic nucleus?

I conjecture that atomic nucleus with $N\approx 250$ particles could be interpreted as a system in equilibrium (maybe the number is too low to consider the use of statistical mechanics as a reasonable ...
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### Introductory text to the Boltzmann equation?

I'm searching for a good introductory text to the Boltzmann equation and how it gets applied in the relativistic case as well?
1 vote
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### I am confused relating Entropy in statistics with thermodynamics [duplicate]

The thing is in thermodynamics we learn entropy as a measure of energy of a system per unit temperature that isn't available for the system to do work. Again, statistically, entropy is a measure of ...
1 vote
42 views

### Do first-order phase transitions necessarily imply hysteresis?

As an example of first-order transition with hysteresis, I am thinking of the magnetization of the subcritical Ising model as a function of the magnetic field. Or density in the liquid-gas transition ...
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### Intuition behind entropy and its differentiation

I was reading the following paper about a better intuition of entropy and how it is connected to heat energy without the use of microstates: The problem is when he assumed that volume is constant and ...
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### Confusion regarding the density operator

I'm confused between two representations of the density operator in quantum statistical mechanics. In the first case, we have : $$\hat{\rho}=\sum_i P_i|\psi_i\rangle\langle \psi_i|$$ In the second ...
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### Energy dissipated by friction and entropy

Can we compute the entropy increase in some simple dissipative systems? Imagine a block sliding on a frictional floor and that its initial kinetic energy is $K$, let's imagine that the ambient ...
1 vote
Suppose I have an electron in a magnetic field given by: $$\vec{B}=B\hat{z}$$ The potential energy of this system is given by: $$U=-\vec{\mu} \cdot \vec{B}=\frac{g\mu_B}{\hbar}\vec{S} \cdot \vec{B}$$ ...
Could someone give me a proof for the entropy of mixing formula, $$\Delta S_{{mix}}=-R(x_{1}\ln x_{1}+x_{2}\ln x_{2}),$$ with $$x_i= \frac{N_i}{N} = \frac{V_i}{V} \ \ ?$$