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

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57 views

Statistical Mechanics Textbook [duplicate]

Although I'll be taking a course on statistical mechanics next term, I'm looking to work through the details of statistical mechanics on my own in the summer. Which textbook would one recommended. I ...
6
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1answer
174 views

Canonical ensemble: correlation function for quadratic potential energy

In this paper I can't understand the following A given system has the potential energy $ U(x_1,x_2,x_3)=k_1 x_1^2 + k_2 (x_2-x_1)^2 + k_3 x_3^2 $. Since the energy is quadratic, the correlation ...
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1answer
50 views

Overcounting and what is indistinguishable about indistinguishable particles?

When getting the overcounting factor in statistical mechanics, how does one compute it? Let's say each property is unique in one aspect (a string with an unique address in pc memory for example). ...
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2answers
38 views

Calculating the Total number of States for a microcanonical system

Please note before flagging, I do not need help solving as the math is simple algebra. Where I am lost is understanding what the math means and why/how it is applied. Problem 2.4 from Reif ...
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0answers
41 views

Link Between the Density Operator and the Partition Function and Boltzmann Distribution in Quantum Statistical Mechanics

I have a very limited knowledge of statistical mechanics, but I seem to running into some related concepts for my background readings for the research project this summer. For example, see the ...
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4answers
139 views

Could you filter coffee back to being pure water?

Okay, so coffee filters remove solid matter from the beverage, whilst leaving the remaining coffee intact for caffeiney goodness. But it's got me thinking. Is there a way we could filter the coffee ...
3
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4answers
303 views

Why would a Boltzmann brain be transient?

The Boltzmann brain idea as I understand it: suppose the universe has an infinite lifetime. Once heat death is achieved, there are no more large-scale structures to the universe -- everything is just ...
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0answers
54 views

Classical Grand canonical partition function derivation

Consider a classical grand canonical ensemble. Let $S_r$ be the reservoir entropy. Suppose it could be expanded at first order: $$S_r \approx S_r(E_t,N_t) + \frac{\mathrm dS_r}{\mathrm dE_i} \cdot ...
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2answers
47 views

Change of variables in canonical probability density

In K. Huang's book Statistical Mechanics, par. 7.2, the author writes the canonical partition function in a different way: $$Q = \frac{1}{N! h^{3N}} \int dp dq \ e^{-\beta H(p,q)} = \int_0^{\infty} ...
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1answer
65 views

What does $f(v)d^3v$ mean?

I am reading the derivation of Langmuir's Evaporation Equation. The author writes: That cylinder contains a volume $dA(vdt)cosθ$ and contains vapor molecules of the designated speed in the ...
2
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0answers
46 views

Density of States for a separable hamiltonian

There are $N$ non interacting electrons in a potential well: \begin{align} H&= -{1 \over 2 } \nabla^2 + U(x,y,z) \\ U(x,y,z)&={1\over2}\omega^2z^2 \; \mbox{for} \; (x,y) \in [0,L]\times [0,L]; ...
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0answers
60 views

Exact Solution of Ising Model in Open Boundary condition

What will be the exact expression of the partition function for 1d Ising model, if we consider open boundary case (This implies that the last spin in the sequence does not interact with the first spin)...
4
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1answer
77 views

Specific heat of the classical ferromagnetic Heisenberg model

I have simulated the classical ferromagnetic Heisenberg model on a cubic lattice using Monte Carlo and I get a finite specific heat near zero temperature. My understanding is that from the magnon ...
15
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7answers
682 views

Relativity of temperature paradox

The imagined scenario: Part A: From special relativity we know that velocity is a relative physical quantity, that is, it is dependent on the frame of reference of choice. This means that kinetic ...
3
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0answers
55 views

Does a theory exist with a symmetry between a tachyonic and non-tachyonic mass points which preserves the normal laws of the mechanic?

Does a theory exist with a symmetry, which mirrors the tachyon mass points to non-tachyon mass points and vice versa? I think, it would be very beautiful, despite that there are strong theoretical ...
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1answer
41 views

Equilibrium in Grand cannonical ensemble

In Grand Cannonical ensemble, where we have a system and reservoir with only energy and particle exchange possible; after $t=0$, there is energy and particle exchange taking place. After equilibrium ...
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50 views

Confusion on meaning of fugacity in scientific publication

in my research project in statistical mechanics, in the context of phase transition and condensation, I was reading the seminal paper of Yang and Lee titled: "Statistical theory of equations of state ...
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1answer
65 views

Does conservation of information mean that the direction of causality is arbitrary? [duplicate]

If it is the case that the information content of the universe is conserved, and the past can be constructed from a complete knowledge of the future just as easily as vice versa, then is there any ...
14
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1answer
210 views

What is the field of mathematics that describes the transition into statistical mechanics?

There are interesting changes that occur in a sample of interacting objects, such as gas particles, as you approach a statistically significant sample. The position or velocity of any given particle ...
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1answer
31 views

Help with understanding result from publication on phase transition

In my current research project in statistical mechanics, in the context of phase transition and condensation, I was reading the seminal paper of Yang and Lee titled: "Statistical theory of equations ...
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0answers
49 views

Average energy from Boltzmann energy distribution is not the same as average kinetic energy of an ideal gas:

The Boltzmann energy distribution represents the probability of a micro-state taking an energy E. It can be formulated as follows: \begin{equation} P(E)=\frac{1}{kT}\cdot e^{-\frac{E}{kT}} \end{...
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1answer
53 views

How to calculate the free energy in curved space?

To study the Hagedorn temperature of string near a black hole, we need to calculate the free energy in curved space. This is can be done calculating a torus path integral, but I want to know if an ...
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1answer
60 views

Hamiltonian - Fourier transform of order parameter [closed]

I have a rather simple task, but it seems I can't move forward with the solution. I have a Hamiltonian as seen in the picture. I have to use the Fourier transform of the order parameter $\phi(x)$ and ...
4
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2answers
138 views

Occupation of quantum states at room temperature

I'm reading up on the physics of degenerate matter (in "An Introduction to Modern Astrophysics" by Carroll & Ostlie, section 16.3), and the impact of electron degeneracy pressure. I came across ...
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2answers
61 views

What VOLUME does exactly the $V$ term in ideal gas equation represent?

According to kinetic theory of gases 'the actual volume occupied by the gas molecules are negligible in comparison to the volume of the container.' I believe that this assumption is significant ...
3
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1answer
137 views

Is it possible to build a logical theory in QM based on quantum logic? [closed]

Quantum Probabilities as Bayesian Probability, Quantum probabilities as degrees of belief Above are two articles about quantum Bayesianism. I don't know why quantum Bayesianism use some results from ...
4
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2answers
107 views

Partition function and coherent state path integral

I have been working through the derivation of the partition function expressed as a path integral in terms of coherent states, following the many-body condensed-matter field theory books of Altland &...
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0answers
30 views

Why do the singularities of the thermodynamic functions expected to be non-negative powers?

I am going through the first chapter of Exactly Solved Models in Statistical Mechanics. On page 4, at the end of section 1.1 it is said that: I would like to know the basis of this expectation. ...
4
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1answer
78 views

The Correct Statement of the Third Law of Thermodynamics

The Third Law of Thermodynamics can be stated in various ways, one of which is: The entropy of a perfect crystal at absolute zero is exactly equal to zero. Is this true for only "perfect ...
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1answer
55 views

Partition sum for $SO(N)$ one-dimensional lattice model

I'm looking for derivation of explicit form of partition function for $SO(N)$ one-dimensional lattice model. The initial expression is $$ Z = \int \limits_{-\infty}^{\infty}d\sigma_{1}...d\sigma_{N}\...
2
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2answers
99 views

Why Boltzmann Entropy's formula is $k_B\log\ W$ and not $0.5\ k_B\log\ W$?

This question is probably wrong - however, I wish to understand even why it's wrong.. Let's take the monatomic gas situation. By the Equipartition theorem, we have that for every degree of freedom ...
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3answers
73 views

Meaning of the phase space in statistical physics

I have a silly question about the phase space. I am confused with the meaning of points in phase space. Does the each point in phase space represent concrete particle of the system, or does it ...
4
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0answers
55 views

Question about Ginzburg-Landau Theory

I was reading CH3 of Reichl's "A Modern Course in Statistical Physics" on Ginzburg-Landau theory and don't really understand a couple of points he makes. He writes: I don't understand why the first ...
3
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1answer
97 views

What is the correlation between QFT and thermodynamics?

This may be a naive question. In physics many processes are symmetric, except a few involving entropy, or the arrow of time. Another one has to do with heat generation. We can generate heat, or energy ...
2
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2answers
71 views

What is the pressure that supports boson star?

What is the pressure that supports boson star? I noticed that for a Bose-Einstein condensate $$ p = k_BT\frac{g}{\lambda^3}\zeta(5/2) $$ where $g$ is the degeneracy and $\lambda$ is the thermal ...
2
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0answers
38 views

When does $E=\frac{3}{2}pV$ hold?

I only know that it holds for classical (monatomic) ideal gas and quantum ideal gas. But does it hold for interacting classical gas (e.g. van der Waals gas)?
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2answers
75 views

Experimental confirmation of the textbook explanation for local entropy reductions

Clarification: In my original wording of this question, regrettably, I did not make it clear that I am interested in the the Boltzmann/Gibbs/statistical (BGS) interpretation of it, as opposed to the ...
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0answers
19 views

Equilibrium states for the Curie-Weiss-Potts model and large deviations

I am doing a project in Large deviation theory applied to statistical mechanics and I was reading this paper http://arxiv.org/abs/cond-mat/0410744. For the general setting we start with a finite ...
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1answer
22 views

Average speed of a molecule in a fermion gas

Starting from Fermi-Dirac statistics, how can be calculated the average speed on the x-axis, $\langle v_{x} \rangle$, of a molecule in a fermion gas a $T= 0\ \mathrm K$?
2
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1answer
95 views

Relation between master, Fokker-Planck, Langevin, Kramers-Moyal and Boltzmann equations

I'm looking for the relation between four important equations which we study in stochastic processes in physics. These equations include Master, Fokker-Planck, Langevin, Kramers-Moyal and Boltzmann. ...
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0answers
32 views

How is zonal flow defined and computed?

The transition to turbulence in pipe flow was recently observed to be in the same universality class as directed percolation. This was done by reinterpreting the turbulence and laminar flow in terms ...
2
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0answers
40 views

Diffusion of carbon monoxide in air

I have been reading about carbon monoxide online. It is lighter than air; Yet, in the case of fire, most online sources claim it spreads evenly throughout a room. Why is this the case? How is it ...
1
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0answers
30 views

Temperature dependent chemical potential

Chemical potential is determined by the number of electrons in the system and coincides with the Fermi energy at zero temperature. The chemical potential can shift as temperature changes if the ...
3
votes
1answer
88 views

Why thermal conductivity increases with temperature?

what is the molecular mechanism with which thermal conductivity increases by increasing temperature? at least for metals? I know that heat increases the oscillations of the atoms in the crystal. But ...
60
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1answer
8k views

If we had a “perfectly efficient” computer and all the energy in the Milky-way available, what number could it count to?

The idea for this question comes from an example in cryptography, where supposedly 256-bit symmetric keys will be enough for all time to come (brute-forcing a 256-bit key is sort-of equivalent to ...
8
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2answers
185 views

Do gravitational waves have entropy?

We know, according the current understanding of black holes and General Relativity, as well as quantum fields in General Relativity, that black holes have an entropy proportional to the area of the ...
0
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1answer
54 views

Fermi energy of electron gas with electrostatic interaction

I have been given the following exam question and am unsure how I would go about solving it: Consider the case of a one-dimensional metal, consisting of a chain of $N$ positive charges $+q$ ...
3
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1answer
69 views

Noise spectrum of the thermal noise?

If we have a thermal noise generated by Brownian stochastic force $\xi (t)$, it has zero mean value. And its correlation function at temperature T is : \begin{equation} \langle\xi(t) \xi(t^{\prime})\...
4
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2answers
88 views

Modern textbook on statistical field theory

What is a good textbook on statistical field theory, with an emphasis on applications to non-equilibrium phenomena? I am a final-year undergraduate, have already taken introductory classes in ...
0
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1answer
59 views

Velocity from the cumulative distribution function of the Boltzmann distribution

I want to get a Boltzmann distribution of the $v_x$, $v_y$ and $v_z$ velocity components (please, notice that the distribution is one-dimensional). To do so, I need the cumulative distribution ...