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

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2
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1answer
42 views

What is the relation between the Boltzmann distribution and Boltzmann equation?

The Boltzmann equation without collision operator $\Omega$ is as follows: $$\dfrac{\partial f}{\partial t} + \mathbf v \cdot \nabla f = 0 \tag{1}$$ Where $\mathbf v$ is the velocity, and $f$ is the ...
-2
votes
0answers
15 views

How are the charges on the plates of a capacitor distributed?

Given a specific overall amount of energy a rectangular parallel plate capacitor stores what number of atoms on a specific plate would have any given specific charge?
1
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1answer
22 views

The expression of the density in terms of molecular mass and the distribution function

I am reading a book about the boltzmann equation, the author gives the expression of the fluid density $\rho$ as follows: $$\rho(\mathbf r,t) = \int {M\,f(\mathbf r,\mathbf c,t) \, \mathrm d\mathbf c}$...
0
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0answers
24 views

How to derive entropy from density of states?

I'm trying to derive the entropy of a black hole, given the density of states of a bosonic string (the details are not relevant). The density of states is $$ \omega(E) = E^\alpha e^{\beta E} $$ The ...
4
votes
2answers
117 views

What is the black hole information paradox really? [on hold]

Preliminaries What is the black hole information paradox really? Is it a sophisticated way to ponder and debate the existence of an operator on the boundary that can tease out the interior of a ...
0
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2answers
48 views

Relation between entropy and internal energy

I am confused as to what is the relation between entropy and internal energy. Entropy is always presented as a measure of the randomness in a system. So when we supply heat to a well insulated system ...
3
votes
0answers
33 views

Is there a block spin renormalization group scheme that preserves Kramers-Wannier duality?

Block spin renormalization group (RG) (or real space RG) is an approach to studying statistical mechanics models of spins on the lattice. In particular, I am interested in the 2D square lattice model ...
0
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0answers
17 views

Landau Diamagnetism and Pauli paramagnetism

In the conventional definition of Landau's diamagnetism we ignore the effect of spin-electron coupling and vice versa for the derivation of Pauli's paramagnetism. I want to know what would happen if ...
0
votes
1answer
47 views

What is the relationship between Maxwell-Boltzmann statistics, Boltzmann distribution and Maxwell-Boltzmann distribution? [on hold]

I have recently been studying some statistical thermodynamics and I am currently trying to understand all the different concepts of the course. I was wondering about differences between MB statistics, ...
2
votes
0answers
22 views

Multi-Cut Matrix Models

I have a question pertaining specifically to a one-matrix model with a multi-cut solution. The standard procedure is to take a polynomial superpotential $W(x)$. In the classical limit (analogous to $...
1
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0answers
18 views

Video lectures for studying graduate level kinetic theory

As the title says it all, I require Video lectures for studying graduate level kinetic theory including but not limited to detailed analysis of viscosity and conductivity, diffusion and Maxwell's ...
1
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0answers
28 views

Specific heat of water

In statistical mechanics, we derive all the thermodynamic quantities, including specific heat $c_v$ from the partition function $Z = \mathrm{Tr} \, [ \, e^{\beta H } \,]$ . For solid, we assume simple ...
0
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0answers
12 views

ploting probability distribution of energy in Canonical ansambel [closed]

To reproducing fig3.3 statistical mechanics pathria, probability density function of energy: $$p(E)\quad \alpha \quad e^{-\beta E} g(E) = e^{-\beta (U-TS)}~ exp{(-\frac{(E-U)^2}{2KT^2C_V})}$$ . I ...
5
votes
2answers
57 views

Books on entropy [closed]

What books introduce entropy in a intuitive, elementary way (at most, for a person with undergraduate physics studies)? The book should not necessarily introduce entropy in relation only to ...
0
votes
1answer
27 views

How to prove that Gibbs state remains a gibbs state after evolution?

Gibbs state is $$ \rho_G=\frac 1Z e^{-H/kT}=\sum_n \frac 1Z e^{-E_n/kT}|E_n⟩⟨E_n|. $$. In wikipedia, it is said that a Gibbs state is an equilibrium probability distribution which remains invariant ...
0
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1answer
38 views

If I prepare a state (density matrix) in Gibbs state, does it go to the lowest energy state at very low temperature?

Gibbs state is $$\rho_G=\frac{1}{Z} e^{-H/kT} = \sum_n \frac{1}{Z} e^{-E_n/kT}|E_n⟩⟨E_n| \, . $$ If $T$ goes to zero, does it mean the $\rho_G$ goes to the lowest energy state $|E_0⟩⟨E_0|$?
0
votes
1answer
78 views

Why Doesn't Einstein Get More Credit for Being the Father of Quantum Theory? [closed]

I'm not simply referring to the notion that Einstein treated the discrete emission and transference of energy (and matter) as "real" physical phenomena, but rather his major continuous role in the ...
-3
votes
0answers
18 views

Moment direction and force [closed]

Replace the three forces acting on the plate by a wrench. Specify the magnitude of the force and couple moment for the wrench and the point P(x, y )where its line of action intersects the plate. FR=...
2
votes
1answer
90 views

Two conflicting forms of equation of state of non-relativistic gas

I've run into two conflicting derivations of the equation of state of a non-relativistic gas. However, the derivations of the relativistic equation of state of both sources agree. I think maybe the ...
1
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0answers
45 views

Mixed Gas Absorbtion

Consider a gas misture that contains two type of atom, A and B. The gas is in equilibrium at temperature $T$. If on the surface of the gas container there are M sites that can absorb an atom gas, and ...
0
votes
1answer
18 views

Water evaporation rate: temperature vs humidity

I have a hot tub which I keep at 100 degrees F, and the water has "a lot" of dissolved salts in it. If I leave it open, will it evaporate faster when it is hot and humid outside, or when it is cold ...
0
votes
2answers
52 views

Canonical partition function and counting

That's a silly silly question, so my apologies, but in this moment I could not reach out! Let's have a system made of a particle reservoir $R$, and a subsystem $S$. The total particle number is $N$. ...
6
votes
1answer
169 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 ...
0
votes
1answer
46 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). ...
0
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2answers
37 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 ...
1
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0answers
39 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 ...
5
votes
4answers
134 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
votes
4answers
294 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 ...
1
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0answers
49 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 ...
3
votes
2answers
43 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} ...
-1
votes
1answer
64 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 ...
1
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0answers
41 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]; ...
1
vote
0answers
55 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
votes
1answer
68 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
votes
7answers
668 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
votes
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 ...
0
votes
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 ...
1
vote
0answers
48 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 ...
1
vote
1answer
63 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 ...
13
votes
1answer
188 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 ...
1
vote
1answer
30 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 ...
0
votes
0answers
47 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{...
1
vote
1answer
51 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 ...
0
votes
1answer
58 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
votes
2answers
132 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 ...
0
votes
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
votes
1answer
134 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 ...
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votes
0answers
27 views

Where can I gain quick access to Path Intergral Monte Carlo?

I am now trying to accomplish a monte carlo simulation on the condensed state of 4He. Yet I am in my sophomore year and know only a bit of quantum statistical physics. Is there any documentations ...
4
votes
2answers
95 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 &...