The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.

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5
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1answer
146 views

Why is it difficult to mix helium and nitrogen gases?

I recently learned an interesting fact: That it's difficult to mix helium and nitrogen gases in a compressed gas cylinder. Gas suppliers that need to mix the two gases have to rotate the cylinders for ...
0
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1answer
34 views

Negative absolute pressure with positive absolute temperature

Could I ask if the derivative defining pressure $dU \over dV$ or ${∂S \over ∂V}|_{E,N} $can be negative in processes occuring in system not cosmological but statistical(gases or solids or liquids-I ...
-2
votes
1answer
55 views

Is there any experimental setup to test if we are Boltzmann brains? [closed]

I am not sure if this subject belongs to mainstream physics. my question is motivated by the fact that I am not sure we could ever test if we are Boltzmann brains. The same happens with string theory, ...
3
votes
2answers
228 views

Can temperature be a complex number?

Is it possible for a temperature to be a complex number? I want to say "no" but I can't be so sure. If it is possible I would like to know of an example. I found an interesting article which treats ...
0
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2answers
82 views

How Statistical Physics?

It's a common fact that in physics, we use statistics (or maybe probabilities ) to describe the behaviour of a system. It was from the statistical analysis of a system where quantum statistics arose ...
0
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1answer
53 views

How can we be sure the Maxwell speed distribution equation is always a rational number?

The Maxwell speed distribution equation is given as $$f(v) = 4\pi \biggl(\frac{m}{2\pi kT}\biggr)^{3/2}\exp\biggl(-\frac{mv^2}{2kT}\biggr)v^2.$$ The left hand side gives the fraction of molecules ...
2
votes
1answer
67 views

Understanding chemical potential in AdS/CFT

I always find it very difficult to understand the notion of chemical potential physically/intuitively unlike pressure and temperature in statistical mechanics. Can some one suggest some nice ...
3
votes
1answer
84 views

Local and global detailed balance

I'm taking a course on nonequilibrium statistical mechanics and I encountered the terms local and global detailed balance. I'm a bit confused about what is their exact definition and what is the ...
0
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1answer
35 views

Bending moment and Shear force

Do bending moment and shear force of a beam depend on it's cross sectional dimentions?? Since all the diagrams which I have draw so far don't involve any cross section details. So I think they do not ...
1
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0answers
30 views

One question about critical exponents for first order transition free energy [closed]

I've got a problem to calculate critical exponents for theory given by Landau free action: $$ \tag 1 L = L_{0} - \frac{1}{2}(\nabla m)^{2} + atm^{2} + dm^{3} + bm^{4} - hm, $$ where $$ -\infty < ...
0
votes
2answers
74 views

Definition of an irreversible process

I'm a little bit confused as to why quasi-static process cannot lose energy to friction in order to be reversible. This is how I'm thinking: Suppose you have a container of gas with a piston, and on ...
0
votes
0answers
39 views

Non-trivial integral with the Bose-Einstein distribution and Cosine function

When I consider the Casimir interaction between an atom and a perfect conducting slab I find the following non-trivial integral: $$\int\limits_0^\infty {\frac{{\cos \left( mx \right)}}{{x + ...
1
vote
1answer
90 views

Is 'Boltzon' an accepted name for particles following Maxwell-Boltzmann (MB) statistics?

In my curriculum during one of my statistical mechanics visiting lecture classes, our teacher was referring comparatively macro particles following MB statistics as "Boltzon". But I have searched ...
1
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0answers
65 views

In the derivation of canonical distribution why does one linearize entropy (and not something else?)

I know that there are (at least) two ways to derive the canonical distribution. I am interested in the one where one considers the entropy of the reservoir (with which the system we are considering ...
0
votes
0answers
27 views

What is normal fluctuation?

I was reading Statistical Mechanics (second edition) by Kerson Huang. On page 146, after equation 7.14, there is a reference to normal fluctuation. What is it? Here is the relevant part from the ...
0
votes
0answers
34 views

Problem in deriving the second term in perturbation expansion the quantum ising model

So I'm trying to derive the perturbation expansion for one particle states in the quantum ising model (Sachdev 2011 QPTs which this is derived from ) $$ H_I= - J g \sum_i \sigma_i^x - J ...
2
votes
1answer
75 views

Boltzmann equation in cosmology

I have a question about the Boltzmann equation in cosmology. Im trying to understand how this can hold? Where does the logarithmic terms come from? It is explained quite well here ...
1
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1answer
149 views

Difference in partition function of classical and quantum Ideal gas

First, I have read this question:What is meant by the term "single particle state" There is an analysis going on in my book (Mandle F. Statistical Physics) that has brought me in a ...
0
votes
0answers
27 views

Work done by a gas in an expansion [duplicate]

1) Consider a gas expanding quasistatically and reversibly from $V_1$ to $V_2$ at constant temperature. I want to calculate the work done. So by convention work done by a system is a negative quantity ...
1
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1answer
42 views

Struggling with whether its $\pm p dV $

I am struggling to understand when calculating the work done by a gas whether it is postive or negative p. It my notes and in many other notes sometimes it is $-pdV$ and sometimes it is $pdV$. I ...
1
vote
1answer
34 views

How can a reversible adiabatic expansion not increase entropy?

In the second stage of the Carnot cycle, a gas is thermally insulated and allowed to expand and do work on the piston. I understand the reason people give is that because entropy is $\,dS = \,dQ/T$ ...
1
vote
1answer
56 views

Changing the zero-point energy

I have the following Hamiltonian $$\mathcal{H}(\{x_i,y_i \})=-l\sqrt{2}\sum_{i=1}^N \mathbf{f}_i \cdot \hat{\mathbf{b}}_i+E_0$$ For calculating things like the partition function it would be ...
1
vote
1answer
60 views

Why the heat capacity doesn't diverge in the Kosterlitz-Thouless (KT) phase transition?

The KT transition has a special properties that, during the phase transition the heat capacity stay finite (so the behaviour of the heat capacity cannot reflect any critical behaviours). However, the ...
1
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0answers
29 views

Find the fraction of atoms in specific quantum state in stellar atmosphere [closed]

Consider gas consisting of hydrogen atoms at temperature about $T \sim 5 \cdot 10^6 \text{ K} \approx 431 \text{ eV}$ and concentration $N \sim 10^{11} \text{ cm}^{-3}$. I need to find the fraction of ...
8
votes
4answers
249 views

Why is the partition function divided by $(h^{3N} N!)$?

When computing partition functions for classical systems with $N$ particles with a given Hamiltonian $H$ I've seen some places writing it as $$Z = \dfrac{1}{h^{3N} N!}\int e^{-\beta H(p,q)}dpdq$$ ...
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0answers
36 views

Thermal Equilibrium of two thin sheets

While reading Gibbs' Elementary Principles in Statistical Mechanics I came across this footnote: The most simple test of the equality of temperature of two bodies is that they remain in ...
0
votes
1answer
37 views

Calculating average quantities in kinetic theory

Consider a volume $V$ with $5$ particles each of mass $m$ at positions $\mathbf{q}_i=(x_i,y_i,z_i) \in V$ and with velocities $\mathbf{v}_i=(u_i,v_i,w_i)$. The speeds of the particles are between $0$ ...
2
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1answer
43 views

Books on Liouville Operator

I am looking for a good book doing classical mechanics and statistical mechanics in terms of the Liouville operator. I have not found a lot on this subject and even books like Mathematical Methods of ...
2
votes
1answer
105 views

Statistical Mechanics vs Statistics

Just how much of a representation of statistics do we get in a statistical mechanics curriculum. What are some of the useful facets of stat not in stat mech/quantum mech that physicists should really ...
3
votes
1answer
285 views

Mean field theory Weiss Approximation for the Isling Model of a Protein

A model for protein in 2D can be formed by adding bonds of fixed length $l\sqrt{2}$ on a square lattice along the diagonal, ie $\hat{\mathbf{b}}_i=\frac{1}{\sqrt{2}}(\pm \hat{\mathbf{x}}\pm ...
1
vote
1answer
90 views

Classifying regions of Van der Waal like gas

Given the equation of state $$p+a\left(\frac{N}{V}\right)=\frac{Nk_BT}{V-bN} \tag 1$$ Taking into account of the fact that a realistic model requires $p \geq 0, V \geq Nb, N>0$ classify the ...
2
votes
1answer
29 views

Derivation for the expectation value of particle density for a pairwise interactions between particles

my question is why is $<\hat{n}(\vec{r})>=n$ I have the Hamiltonian $H_N= \sum_{i}^{N} \frac{P_i^2}{2m}+U(\vec{R_1},\vec{R_2},..,\vec{R_N})$ where $U(\vec{R_1},\vec{R_2},..,\vec{R_N})= ...
0
votes
1answer
60 views

How do you go from a sum over frequencies to an integral?

I am trying to figure out how to go, with help of a density of states function $g(\omega)$, from a sum like this $$K=\sum \limits_{j=0}^N f(\omega_j)$$ to an integral over the frequencies for $N \to ...
0
votes
1answer
46 views

Meaning of solutions of an equation of state [closed]

Question Let $p \geq 0, V \geq Nb, N > 0$. Now we are given the equation of state $$p+a\left(\frac{N}{V}\right)=\frac{Nk_BT}{V-b} \tag 1$$ Classify the solutions of the equation of ...
0
votes
1answer
32 views

Problem with indistinguishability in partition function

Consider an ideal gas of classical particles of mass $m$ in uniform potential $\xi$ in 3d. The gas $N$ molecules, volume $V$ and is at temperature $T$. I believe that the Hamiltonian of this system is ...
1
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1answer
46 views

Deriving pressure from a given partition function

If the partition function for some system is given as $e^{\text{$\alpha $T}^3V}$; please note note that $\alpha$ is a constant. I have computed $$\left[\frac{\text{$\delta $Z}}{\text{$\delta ...
1
vote
1answer
26 views

bridging the connection from the Helmholtz free energy in classical thermo to stat mech

The Helmholtz-free energy from classical thermo is defined as $$\text{F=u-TS}$$ taking the differential and algebraic manipulation, we arrive at $$\text{dF=-pdv-sdT}$$ Observe that: ...
1
vote
1answer
79 views

Strange vector matrix operation (in “A Modern Course in Statistical Physics” by Reichl)

I am reading "A Modern Course in Statistical Mechanics" by Linda E. Reichl. Where i encountered this notation: $$\Delta S = \bar g : \vec \alpha \vec \alpha$$ Here $\bar g$ is $$ g_{i,j}=-{ ...
1
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1answer
34 views

What is the definition of 'relative population' in context of partition function?

In statistical mechanics, what is the definition (or mathematical definition) when authors refer to relative population in the case of a classical particle system?
0
votes
1answer
47 views

is it necessarily true that the partition function $Z$ (with degeneracies) $ =1$?

The partition function with degnerate energies is $$\text{Z}=\sum _ig_ie^{{-E_i}/{k_BT}}.$$ Because the partition function Z is defined as the normalisation constant, does Z always = 1?
2
votes
1answer
110 views

The energy contribution of a frequency at finite temperature

This is from a paper I'm reading: Since each frequency contributes $\hbar \omega/2$ of energy (or at finite temperature, $\hbar \omega /2 \coth(\hbar\omega/2kT)$), we can find the energies for the ...
1
vote
1answer
145 views

How do we find the phase space density from the Hamiltonian?

How do we find the phase space density from the Hamiltonian? For example: Consider a classical gas made of N identical non-interacting particles in 1d. Each molecule is characterised by centre mass ...
1
vote
1answer
56 views

The grand partition function of non interacting hamiltonians

In the case of non interacting particles I know we can write the Hamiltonian as $$H(\mathbf{q}_1,\dots,\mathbf{p}_1,\dots)=\sum_{i=1}^N h(\mathbf{q}_i,\mathbf{p}_i)$$ but I am having trouble ...
0
votes
0answers
51 views

Finding the phase space density of $N$ harmonic oscillators

Consider a system of $N$ identical harmonic oscillators in 1d. The Hamiltonian will be given by $$\mathcal{H}_N=\sum_{i=1}^N \frac{p_i^2}{2m}+\frac{m\omega^2}{2}q_i^2$$ Now supposedly the Hamiltonian ...
1
vote
1answer
47 views

Are there any units involved in the partition function for a classical particle system?

Is the output of a partition function dimensionless or are there units involved? The question as it is: $$E_1\text{=0}K_B\text{,g=1}$$ $$E_2\text{=0}K_B\text{,g=3}$$ $$E_3\text{=0}K_B\text{,g=5}$$ ...
4
votes
1answer
81 views

What happens to the planck distribution if the temperature is set to zero?

BE Problem I am currently working on modelling the density of states and optical conductivity of graphene utilizing the GW algorithm. In calculating the exchange self energy of the system, the ...
0
votes
1answer
21 views

Phase correlation between an excited and ground state in a BEC

What happens to the phase of the atom that gets kicked out of the atomic condensate? Is it completely random or does it have some correlation with the condensate phase?
0
votes
1answer
87 views

Topological entanglement entropy in transverse quantum Ising model?

I have seen from literature that the $Z_2$ lattice gauge theory in 2d could be mapped into a quantum Ising model with gauge constraints on the Hilbert space by dual transformation. The deconfined ...
1
vote
2answers
78 views

Conceptual explanation of the Single particle partition function

The Single particle partition function is defined mathematically as $$\text{Z=$\sum $}g_ie^{\left(\frac{-E_i}{K_BT}\right)}$$ But what is the physical interpretation of the partition function and ...
1
vote
0answers
55 views

How can I compute the average number of collisions of a particle in a spherical container? [closed]

I have to compute the average number of collisions per unit time of a particle in a spherical container. These collisions are diffuse, i.e., after colliding, the particle bounces off the inner walls ...