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

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250 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 ...
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4answers
219 views

Is thermodynamic free energy and potential energy the same thing?

The equation for free energy $F$ and potential energy $E_{pot}$ are: $$ F=U-TS \\ E_{pot} = E_{tot} -E_{kin} $$ But the temperature $T$ is proportional to the average kinetic energy of a system. So ...
2
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1answer
117 views

H-theorem and Boltzmann equation applied to Boltzmann distribution

Using the Boltzmann equation: $$ \frac{dH}{dt} = \int_0^{\infty} dr \int_0^{\infty} ds W(r,s)[p_r - p_s][\ln{p_r} - \ln{p_s}],$$ and assuming $p_r = e^{-\beta r}$, the equation looks like $$ ...
3
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3answers
280 views

In what limit do we *really* get Maxwell-Boltzmann statistics from Bose-Einstein and Fermi-Dirac?

Fermi-Dirac and Bose-Einstein energy occupation number $n(\epsilon)$ in natural units ($[T]=[\epsilon]$) read $$n(\epsilon) = \frac{D(\epsilon)}{e^{(\epsilon-\mu)/T}\pm 1},$$ where $D(\epsilon)$ is ...
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2answers
330 views

Fermi-Dirac Statistics

In Fermi-Dirac statistics the probability of being in a certain energy state is $$f(E) = \left[1 + \exp\left(\frac{E-E_F}{k T}\right)\right]^{-1}$$ In the area that I'm looking at the texts always ...
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1answer
52 views

Ising model 2-dimensional - ground state configuration

I have to prove something about the 2-dimensional ising model. The problem is the following: Prove that every nearest-neighbour and next-nearest-neighbour interaction on the square lattice ...
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1answer
36 views

Canonical Distribution (Partition Function)

For the canonical distribution $$ w_{n}=e^{(F-E_{n})/T}, $$ is the sum $$ Z=\sum_{n}e^{E_{n}/T} $$ a sum over energies or a sum over states? Perhaps this is a silly question, but Landau and Lifshitz ...
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1answer
55 views

Spontaneity / Free Energy of Non-Isothermal Process

I'm trying to determine a lower bound for the work input necessary to make an entropy-reducing process "spontaneous" in the sense that the 2nd law is not violated. For a constant temperature and ...
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1answer
26 views

Simulating Phase Space Evolution

I am interested in modeling the time evolution of phase-space $\rho(\vec{q},\vec{p},t)$. I have attempted to use Liouville's theorem $\partial_t\rho=-\sum_{i=1}^{3}(\partial_{q_i}\rho)\dot ...
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0answers
30 views

Applying Statistical Mechanics to Formulate Corrosion (Rusting)

I wanted to try and take my current knowledge of statistical mechanics (first quarter undergraduate course completed, beginning researcher in far from equilibrium statistical mechanics, basic ...
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0answers
18 views

How to find Entropy of system in terms of Magnetic Field and Temperature

I'm studying for final exams and I have a question about how to find the entropy of a particular system. The system is a lattice of paramagnetic atoms fixed to the lattice sites, with an external ...
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1answer
23 views
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1answer
30 views

Periodic ground state 1-dim ising model

Good evening! I'm at the beginning of my study about the Ising model and it has been proposed to me this problem: Find all periodic ground-state configuration for the following one-dimensional Ising ...
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0answers
29 views

How can one approximate integral def. of Z by the max value of the integrand?

I am taking a course in statistical physics, and while reviewing my notes from the lectures I came across something that I cannot get my head around. We arrive at an integral expression for the ...
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1answer
35 views

Subtraction In Quadrature?

I have a system of particles (electrons) with an initial RMS energy spread (say "1"). It goes through a section of constant magnetic field (bend magnet) and the electrons radiate. The electrons lose ...
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1answer
190 views

Virial Theorem and the Energy in a Gas

I clearly am interpreting the Virial Theorem incorrectly, but I don't know how. In dipole gases, the molecules can exhibit five kinetic modes, while they can only experience 2 potential modes. Doesn't ...
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1answer
23 views

Change in entropy adiabatic expansion

I think that an adiabatic expansion of a gas should cause the entropy to increase. On the other hand we have for adiabatic processes that $dQ = 0$ and therefore $dS= 0$, which is why I thought that ...
6
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1answer
63 views

Minimum connectivity required for mean field to be a good approximation?

In spin models, it is known that mean field becomes a better approximation as the connectivity increases. My question is: Is there an estimate for the threshold connectivity (as a function of the ...
3
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1answer
76 views

Simple estimation of the critical temperature of water

I'm trying to develop fermi estimation skills and I came up with a question for which I don't even know where to start from. Here goes: Is it possible to estimate the critical temperature (say in ...
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2answers
53 views

From Quantum Mechanics to Statistical Mechanics in a Specific Case

I'd like to know how to get to statistical mechanics from the many-particle Schrodinger equation using a specific example, without using any Hamiltonian mechanics, phase spaces or ensembles, as a ...
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3answers
269 views

Does entropy have a physical meaning?

Entropy is incredibly useful as a mathematical tool. But what does it actually mean? I understand that the Boltzmann entropy is defined by: $$S=k\ln{\Omega}$$ With $\Omega$ being the multiplicity ...
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1answer
41 views

chemical potential in BEC decreases in temperature

For a bose gas we can calculate the average number of particles through $$N = \int_0^\infty \rho(\varepsilon)n(\varepsilon) d\varepsilon$$ where $\rho(\varepsilon)$ is the particle density for energy ...
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3answers
48 views

Change in energy ideal gas

I am supposed to calculate the change in energy upon changing both the temperature from $T_1$ to $T_2$ and the volume from $V_1$ to $V_2$. Now I was wondering whether this solution is correct: We ...
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2answers
65 views

First law of thermodynamics [closed]

In the first law of thermodynamics, we learned that $W$ and $Q$ are path-dependent quantities, but how are $Q$ and $W$ defined? I mean $W = \int_{\gamma} p(s) ds$ would be one possibility, where ...
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1answer
62 views

Ising model on lattices with (vertical side length) $\neq$ (horizontal side length)

Consider the Ising model with nearest neighbours interactions on a rectangular lattice $L\times M$. If $L=M$ (2-dimensional square lattice), it is known (e.g. by Peierls argument or Onsager explicit ...
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1answer
75 views

Spin version of Maxwell's demon: Where's the energy?

I have confused myself about the following variant of Maxwell's demon and I can't seem to find out where the energy went. Consider this: You have a chain (one dimension) of spins (up/down) with a ...
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4answers
2k views

Exorcism of Maxwell's Demon

I am possessed! Yes, with the thinking that if there is actually a Maxwell's Demon, then it would open the negligible weighted door which would ultimately make the second law invalid. But really can ...
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2answers
74 views

Does QM needs refinement?

Suppose atoms of an ideal gas are represented by non overlapping wave function so that the system can be described classically. As time passes the packets spread. Therefore over a period of time we ...
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0answers
19 views

Volume in NVT ensemble

While solving a problem of ideal gas in canonical ensemble, I got stuck into this one. It may sound silly though- Why $$\int d^{3N}q$$ equals to $V^N$ but not $V^{3N}$
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15 views

Schottky Anomaly - Heat Capacity

I'm having a little bit of a difficulty understanding the origins of the schottky anomaly at low temperatures in the heat capacity of certain materials with restricted energy levels. As I understand, ...
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2answers
372 views

Renormalization Group and Ising with d=1 and D=1

I have a question about the results of RG on Ising model. I know it's possible to obtain two couple of relations $K'(K)$, $q(K')$ $K(K')$, $q(K)$ between the coupling costants. My problem arise ...
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1answer
61 views

Debye Model Density of States In One Dimension

I am trying to obtain the Density of states of the Debye model in one dimension I know the answer I am prepping for an exam and I am a bit stuck: The answer is: $\frac{L}{\pi*c_s}$ where $c_s$ is ...
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1answer
44 views

What is the density operator for an isothermal–isobaric ensemble (T,p,N)?

In the microcanonical ensemble $(E,V,N)$, the density operator is $$\hat{\rho}=\frac{\delta(\hat{H}-E\,\hat{I})}{Tr(\delta(\hat{H}-E\,\hat{I}))}$$ Where $\hat{H}$ is the Hamiltonian of the system and ...
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21 views

Independent boson model with an arbitrary finite-dimensional impurity

The independent boson model consists of the following Hamiltonian: $$ H_s = E \sigma^z $$ $$ H_b = \sum_k \omega_k b^{\dagger}_kb_k $$ $$H_{sb} = \sigma^z \sum_k (g_k b_k + g_k^{\ast}b^{\dagger}_k).$$ ...
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3answers
4k views

Is there any proof for the 2nd law of thermodynamics?

Are there any analytical proofs for the 2nd law of thermodynamics? Or is it based entirely on empirical evidence?
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70 views

How to derive the critical temperature for Bose-Einstein condensation of photon?

I found in Nature magazine that photon can have Bose-Einstein condensation. But I have a question how to derive the critical temperature for photon? Because the chemical potential of photon is zero ...
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1answer
71 views

What does Born Green equation signify physically?

What does Born Green equation obtained from YBG hierarchy for the equilibrium particle densities signify? I mean how can you model the equation into a physical problem?I understood the steps involved ...
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1answer
56 views

A simple experiment and the Maxwell-Boltzmann distribution

Consider two containers separated by a removable wall, each side of which is a perfect mirror for the gas in the respective container. Also the walls of the containers are ideal mirrors. In each ...
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2answers
95 views

What is an intuitive explantion for the fact that the Maxwell-Boltzmann distribution of energies is independent of mass?

If you take the Maxwell-Boltzmann distribution of velocities (which depends on the mass) and substitute $v=\sqrt{\frac{2E}{m}}$ you get the distribution for the energies, which turns out to be ...
3
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1answer
84 views

What it means to integrate over $n$ variables out of $N$, where $N>n$?

I was reading Theory of Simple Liquids, when I came across BBGKY hierarchy. In deriving the expression for the hierarchy, they integrate an integration of N variables over N-n variables to make the ...
5
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1answer
48 views

How does the movement of molecules change at the edge of a liquid?

I am thinking about how the velocity of molecules measured from a small region of space might change as the region of inquiry moves closer to the edge of a container. Ultimately I am thinking about MR ...
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2answers
87 views

Thomas - Fermi screening

I read in Ashcroft & Mermin's Solid State text that for the Thomas-Fermi approximation to be applicable, the external potential needs to be "slowly varying," What does it mean for a function (in ...
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1answer
58 views

Which function denotes the energy of thermal motion within a system?

In thermodynamics, the heat $Q$ is defined as a type of energy in transfer, and is not a state function, which function denotes the energy of thermal motion within a system? 1) $TS$, (there is a ...
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1answer
119 views

Thermodynamics, chaperones : How to model polymer fragmentation

Living polymers are well described by equilibrium statistical physics. Now I would like to consider a case were living polymers undergo fragmentation due to chaperones. I can think of a kinetic ...
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0answers
70 views

Calculate Helmholtz Free Energy with Entropy, Work given [closed]

it's my first time here and I hope the post complies with the general rules. My problem originates here: I'm doing a statistical physics task which unfortunately leaves me clueless atm. I keep my ...
3
votes
1answer
82 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf ...
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1answer
62 views

Maxwell's Inspiration to think about fields

I was looking at a Wikipedia article which had the following statement Atomists, notably James Clerk Maxwell and Ludwig Boltzmann, applied [...]. In modern literature Maxwell is often thought ...
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26 views

Johnson Noise: Source of thermal fluctuations

I've read a lot online about Johnson noise being caused by thermal fluctuations, and the Wikipedia page of thermal fluctuations attributes this to the fact that particles don't all have the same ...
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2answers
22 views

How velocity dispersion changes with change of inertial frame

I'm analysing a bunch of simulated galaxies, and one of the properties I'm looking at is their velocity dispersion (which is the same thing as the standard deviation of their speeds as far as I know). ...
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1answer
32 views

How did Planck use the concept of statistical entropy in trying to understand the meaning of his own law?

I was reading Introducing Quantum Theory: A graphic guide (by J.P.McEvoy & Oscar Zarate) and came across Planck's predicament of understanding his very own law that accurately explained the ...