# 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.

3,300 questions
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### Escaping metallic solids under extreme pressure

Suppose you have metallic solids inside an indestructible tube, with a very powerful and indestructible piston - the piston gets a tiny hole on the piston. What would happen if you compress the solid ...
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### Kosterlitz-Thouless transition and correlation function

I’m studying Kosterlitz transition on this book: https://tinymachines.weebly.com/uploads/5/1/8/8/51885267/kardar._statistical_physics_of_fields__2007_.pdf#page173 . At page 165 it says:” The gradient ...
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### What is meant by finite harmonic oscillator?

What does it mean to take finite harmonic oscillator, In research article "http://iopscience.iop.org/article/10.1088/1367-2630/17/11/113015 ", we were finding effective number of cobosons in ...
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### Can we say that density matrix gives probability?

In statistical physics Boltzmann probability is given by $$P= \frac{\exp(-\beta E_i)}{\sum_i\exp(-\beta E_i)}$$ whereas we can also write it $$\rho= \frac{\exp(-\beta H_0)}{\sum_i\exp(-\beta H_0)}.$$...
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### Spin spin correlation function in topological phase transition?

during my vacation i have decided to study Kosterlitz and thouless phase transition (i have already posted 2-3 questions about that). I don't know quantum field so I did not expect to understand ...
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### What is bose enhancement factor?

I am studying about composite bosons ,when we write N state for composite bosons in terms of its constituent particles, we add factor of normalization constant \chi in denominator.This normalization ...
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### Integrating Carnahan-Starling Pressure

Given the Carnahan-Starling equation of state for a solution of hard-spheres, $$Z = \frac{P}{\rho k_BT} = \frac{1 + \eta + \eta^2 - \eta^3}{(1-\eta)^3}$$ where $\rho = N/V$ is the number density and ...
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### Laplace Transform Density of States & Partition function

I am currently going through Pathria's Statistical Mechanics text , and under the Canonical Ensemble description, the author stresses that the partition function of a continuous system is the Laplace ...
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### Computing the average energy $\overline{E}$ in thermodynamic equilibrium for a paramagnet

I am having trouble with the following physics exercise: In the case of a paramagnet in a magnetic field $H$, show that from the requirement that $F(E)$ (the Helmholtz free energy) be minimal in ...
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### Canonical partition function for different systems

As a homework exercise for Advanced Statistical Mechanics I need to derive the canonical partition functions for the following systems: Single component ideal gas on a square lattice Single component ...
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### What is the link between statistical and QFT correlation functions?

I'm studying statistical mechanics in particular correlation function: https://en.wikipedia.org/wiki/Correlation_function_(statistical_mechanics) and I have understood it. Now searching on internet ...
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### Computing the Helmholtz free energy for a harmonic oscillator

I would like to calculate the helmholtz free energy for a harmonic oscillator, which has energies given by the equation $\epsilon_{n} = n\hbar\omega$, where $n$ is a natural number greater than or ...
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### Venturi effect on molecular level

Is there a good explanation why the pressure becomes lower on the narrow part of the venturi pipe? I'm not interested in the newton explanation or pressure differences explanation. I want to ...
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### In Boltzmann distribution, why is the system at the same temperature as the reservoir?

Consider a boltzmann distribution where the total energy of the reservoir and the system is $E$. The energy of the system can be $\epsilon_i$ and the energy of the reservoir is $E-\epsilon_i$. Now ...
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### From emission probability to black body spectrum. (Hawking radiation as tunnelling.)

In the 1999 paper by Wilczek & Parikh (and in many subsequent papers) the "emission rate" (really the probability of tunneling) of a particle with energy $\omega$ from a static black hole (BH) is ...
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### Would it be appropriate to say that in presence of Non-Conservative Forces, the Entropy of System Always Increases?

Would it be appropriate to say that in Presence of Non Conservative Forces the Entropy of a system would always increase? Can we relate Non-Conservative Forces and Entropy in some way? I intuitively ...
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### Why are the Lyapunov and Lindeberg Central Limit Theorem conditions often satisfied in the real world?

Some background for the question. I've been trying to understand why so many things have a Gaussian Distribution. There are a lot of questions about this on StackExchange but none of them were ...
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### Computing the average energy and specific heat at constant volume

Consider an Einstein solid. Each oscillator has quantized energy $E = n\hbar\omega$, where $n \geq 0$ is an integer. How can I compute the average energy and the specific heat at constant volume of an ...
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### Bose Einstein Condensation in Grand canonical ensemble

Why we develop formalism of Bose Einstein Condensation in framework of grand canonical ensemble ?
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### $dQ=Tds$ and quasistatic process

See Ján Lalinský's commment on Entropy $dQ=TdS$ and Work $dW = -pdV$ conditions? My question are: Is there a way to prove that $dQ=Tds$ is a quasistatic process? What's the funcitonal description ...
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### Deriving an entropy expression from two other expressions

I would like to show that an equation for entropy is given by $$S = k\frac{\partial}{\partial T}\left[T \ln Z\right].$$ I am given the equations $$S = -k_{B}\sum_{i = 1}^{N} p(n_{i})\ln(p(n_{i}),$$...
Using the thermodynamic definition of temperature, $$\frac{1}{T}=\frac{\partial S}{\partial U}\bigg|_{V,N}$$ negative temperatures are possible, in systems where the entropy decreases when energy is ...