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

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108 views

What is the physical interpretation of the Papadodimas/Raju mirror operators?

In this paper http://arxiv.org/abs/1310.6335, the authors discuss the firewall problem and contruct so called mirror operators appearing in the correlation function. The key part seems to be (2.6) ...
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1answer
110 views

'Fermi-Dirac'-like occupation probability at high temperature

Consider an ensemble of $N\to\infty$ free particles, each of which can assume energy states $E_i\in\{0,E\}$. Using the canonical ensemble one can compute the occupation probability for a single of ...
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1answer
454 views

Partition function for a microcanonical ensemble

Is it possible to write down a partition function for a microcanonical ensemble?
2
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1answer
221 views

Probability of finding n particles in a volume v

I'm trying to calculate the probability of finding $n$ particles in a certain volume $v$ in a system with a total of $N$ particles and total volume of $V$. My problem is that I've tried two approaches ...
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1answer
120 views

Questions about Statistical Mechanics

For grand partition ensemble, is it true that the introduction of chemical potential allows us to have the sum of number of the particles in each state to be the total number of particles ("On ...
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2answers
81 views

Non-Equilibrium Statistical Mechanics

Can anybody please explain what is the difference between equilibrium state and steady state, as quoted by book by Degroot and Mazur. Also, does violation of Principle of Detailed Balance means the ...
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2answers
217 views

Meaning of the chemical potential for a boson gas

My lecturer told me that the mu is the Chemical potential is zero or negative, in the following example, mathematically it acts as a Normalisation constant. But is there any Physical insight about why ...
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1answer
82 views

Density of states (treating states in continuum)

If we have a particle in a 3D infinite square well box, with length $L$, e.g. an electron in a conduction metal. By solving the Time independent Schrodinger equation, we can get the formula of ...
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2answers
95 views

Where does the Maxwell-Boltzmann distribution come from?

I understand that Maxwell-Boltzmann distributions arise for distributions of weakly interacting particles at equilibrium. But I'd like to know if there's a deeper reason behind why they are ...
4
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1answer
99 views

Do we have a fundamental Hamiltonian for the system of H$_2$O molecules?

From the quantum mechanics(QM) viewpoint, does there exist a Hamiltonian $H$ for the system of H$_2$O molecules? Assume that the number of H$_2$O molecules is fixed. Imagine that by calculating the ...
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0answers
40 views

Find out ground sates for large 2D classical spin model

Reaching the ground state of a large 2D classical spin model (e.g. classical Heisenberg model) might be a relatively difficult task while using conventional "flip/reject" Monte Carlo method. The ...
0
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2answers
128 views

Quantum Quench Problem

I read about the quantum quench problem in condensed matter physics. But what does really mean? Has anybody a good explanation about the origin of quantum quench problem?
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2answers
89 views

Probability of having energy $E$ when $E$ is bounded

For a canonical ensemble the probability of a system to have energy $E$ is $P(E)=e^{-\beta E}$. For that we consider the that the system can have any energy between $0$ to $\infty$. What will be the ...
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1answer
145 views

A question about Fermi-Dirac Distribution function

It seems more like a mathematical question, about the property of Fermi-Dirac Distribution function $$f=\frac{1}{e^{(E-\mu)/k_BT}+1}$$ where $\mu$ is the chemical potential and $k_B$ is the Boltzmann ...
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2answers
209 views

Planck's distribution and Bose-Einstein distribution?

If the application of the Bose-Einstein distribution is in blackbody radiation, then what is Planck's distribution? Are they same? How did Planck know that he should use a Bose-Einstein distribution ...
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1answer
128 views

What is “number degrees of freedom for frequency ν”. Frequency is 1D right?

The book QM Demystified states this about black body radiation spectrum: An attempt to explain these results using classical theory was codified in the Rayleigh-Jeans formula, which is an ...
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1answer
127 views

Grand canonical ensemble: 0 particle state

The partition function of the grand canonical ensemble can be generally stated as $$ \mathcal{Z} = \sum_{r} e^{-\beta(E_{r} - N_r\mu)}\tag{1}$$ where $E_{r}$ is the energy of the micro-state $r$ of ...
5
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1answer
122 views

Why Landau Level quantization is observed only in low temperature and strong magnetic field in real experiment?

I know that Quantum Hall Effect and Fractional Quantum Hall Effect origin from Landau Level quantization. In magnetic field, the energy of in-plane(plane perpendicular to magnetic field) degree of ...
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1answer
103 views

${1 \over T} e^{-i/T}$ for Bolzmann-Gibbs distribution

There is a book from Tom Carter on entropy. In the Economics I application (page 111), he ingeniously computes that the distribution of fixed amount of M money over N individual tends to $$p_i = {1 ...
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1answer
93 views

Quantum Mechanics mistake in partial trace

I have a given a density matrix by $\rho:=\frac{1}{2} |\psi_1 \rangle \langle \psi_1|+\frac{1}{8} |\psi_2 \rangle \langle \psi_2|+\frac{3}{8} |\psi_3 \rangle \langle \psi_3|.$ Where $|\psi_1\rangle ...
2
votes
1answer
106 views

Why do we get the same result using different ensembles?

There are different kinds of ensembles: microcanonical, canonical, grand-canonical... But for a particular system, no matter whether the system is isolated or closed, they just give the same result of ...
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1answer
108 views

Ensemble average of product of spin operators?

How do you evaluate the canonical ensemble average of a product of spins, e.g.: $$[S_zS_x]$$ Where: $$S_x = \frac{\hbar}{2} \begin{pmatrix} 0 & 1\\ 1 & 0\\ \end{pmatrix}$$ $$S_y = ...
3
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2answers
544 views

What are the key properties of and differences between classical and quantum statistical mechanics?

I'm studying different ensembles and different statistics (M-B, B-E, F-D), and I have some ambiguities about which of these models are applicable to quantum systems and which are usable for classical ...
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0answers
28 views

Statistical mechanics prerequisite [duplicate]

I`ll be taking senior level and graduate course in statistical mechanics in a month. I was wondering what would be the best statistics and probability textbook to prepare for it? I`m currently ...
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1answer
59 views

How to calculate the exchange constant of the Ising model?

The Ising model is a mathematical model of ferro-magnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic spins that can be in one ...
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1answer
296 views

How to derive Stefan constant from Planck's Blackbody radiation?

How to derive Stefan constant from Planck's Blackbody radiation? Consider the following expression relating to blackbody radiation: $$\phi(\lambda) d\lambda= E({\lambda}) \, ...
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1answer
34 views

Gap exponents and homogeneous functions

Looking at this paper on page 1 how is the first limit obtained? That is, if I have some homogeneous function $g_f(h/t^{\Delta})$, how does setting the gap exponent $\Delta$ to $3/2$ ensure that ...
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1answer
139 views

Confusions regarding entropy

Help, I am terribly confused about entropy. On the one hand, I am taught at school that a substance such is an ice/solid has a lower entropy than its gaseous equivalent and that a process such as ...
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1answer
240 views

Using the Maxwell-Boltzmann distribution function to find specific molecule speeds?

I've been looking for problems to practice on this topic and found a problem asking to use the Maxwell-Boltzmann distribution function to calculate the fraction of Argon gas molecules with a speed of ...
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1answer
109 views

Can exergy and exergy destruction be understood through thermodynamical and/or statistical-mechanical principles?

My textbook Fundamentals of engineering thermodynamics, Moran and Shapiro states: The exergy is the maximum theoretical work obtainable for an overall system consisting of a system and the ...
5
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3answers
153 views

Physical intuition for independence of components of velocity in derivation of Maxwell–Boltzmann distribution

Maxwell derived the shape of the probability distribution of velocity of gas particles by starting with just two assumptions. These are: The probability distribution is rotation invariant. The ...
3
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1answer
389 views

1D Ising Model (NN and NNN interactions) with 2 transfer matrices

I've tried an alternative solution for finding the partition function of this model. So is what I've done correct? If it isn't then please prove and explain why not. (I'm pretty sure I made a ...
2
votes
1answer
77 views

Does non-conservation of number of particles imply zero chemical potential?

In the systems like photon gas in a cavity and phonon gas in a solid number of particles is not conserved and chamical potential is zero. Is this a general rule? If yes, how zero chemical potential is ...
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0answers
137 views

Math needed for undergrad Statistical Mechanics/Thermal Physics

A professor recommended me to take a course on Statistical Physics as preparation for agent-based computing in social sciences. Now I have no experience in physics beyond basic highschool, and ...
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2answers
125 views

Reference request for exactly solved models

Can someone recommend a textbook or review article that covers exactly solved models in statistical mechanics, such as the six- or eight-vertex models? If there is literature at the undergraduate ...
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1answer
57 views

In calculating entropy, why can the partitioning of an ensemble into microstates be chosen “somewhat arbitrarily”?

I'm confused by statistical entropy. It seems to me like the number of microstates for a given macrostate would increase without bound as finer partitionings of the phase space are chosen. Why is it ...
27
votes
4answers
693 views

How exact is the analogy between statistical mechanics and quantum field theory?

Famously, the path integral of quantum field theory is related to the partition function of statistical mechanics via a Wick rotation and there is therefore a formal analogy between the two. I have a ...
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0answers
77 views

Free path distribution

I'm studying statistical mechanics, and I'm trying to resolve some problem known from my thermodynamics course. So I want to calculate mean free path for particles with a concentration $n$ and ...
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1answer
214 views

Partition function for classical particle and quantum particle are the same?

Permutation for classical particle $$\Omega=\frac{N!}{\Pi n_i!}$$ By using Lagrange method of undetermined multiplier, we get $$n_i=Ae^{\frac{-E}{kT}}$$ Probability, $$p=\frac{n_i} {Z}$$ where we ...
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1answer
109 views

Semiclassical Approximation

In many books I read about semiclassical approximation applied to the field of Bose-Einstein condensation. But I don't understand what it really means. For example I read that an expression like this ...
9
votes
1answer
240 views

Motivation for the use of Tsallis entropy

Every now and again I hear something about Tsallis entropy, $$ S_q(\{p_i\}) = \frac{1}{q-1}\left( 1- \sum_i p_i^q \right), \tag{1} $$ and I decided to finally get around to investigating it. I haven't ...
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2answers
344 views

Probability of Different States - Canonical Ensemble - Partition Function

Consider a canonical ensemble of $N$ ideal gas atoms, which could have spin up or spin down. Why is it that the probability of finding the particle in a spin up state generally only involves the ...
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0answers
146 views

Average number of spin up particles

In a paramagnetic system, where $N = N_\uparrow + N_\downarrow$ is fixed, how does one calculate the average number of spin-up particles $\langle N_\uparrow \rangle$? You can assume we have the ...
2
votes
1answer
424 views

Partition Function for Two Level System

I have a system with $N_s$ sites and $N$ particles, such that $N_s >> N >> 1$. If a site has no particle, then there is zero energy associated with that site. The $N$ particles occupy the ...
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0answers
328 views

Is Feynman talking about the Zeroth Law of Thermodynamics?

In Volume 1 Chapter 39 of the Feynman Lectures on Physics, Feynman derives the ideal gas law from Newton's laws of motion. But then on page 41-1, he puts a caveat to the derivation he has just ...
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2answers
138 views

Paramagnetism and large N

In a paramagnetic system, we have: $$N = N_\uparrow + N_\downarrow$$. If we have a large system, with $N >> 1$, is it generally okay to assume $N_\uparrow \approx \frac{N}{2}$ and ...
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3answers
172 views

Distinguishable, Indistinguishable Paramagnetic Ideal Gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
2
votes
1answer
83 views

Can I express the heat flow of a fluid in terms of estabilshed characteristics of the velocity distribution?

If $\rho$ is the mass density of a fluid and $A({\bf v})$ is an function of the velocity, which is distributed according to $f({\bf v})$, we have an averaging process $A\mapsto \langle A\rangle:=\int ...
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1answer
93 views

General way to model baths? Harmonic Oscillators valid?

I am trying to model an open system interaction without making strong assumptions on coupling strength or temperature. In general i understand that open systems are modeled by a Lindbladian, but as ...
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174 views

Can Lee-Yang zeros theorem account for triple point phase transition?

Now the prominent Lee-Yang theorem (or Physical Review 87, 410, 1952) has almost bocome standard ingredient of any comprehensive statistical mechanics textbook. If the volume tends to infinity, ...