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

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76 views

Has anyone studied a statistical scaling law for the universe? [closed]

How do named objects in the universe scale? Is there a predictable curve for an ordered list, say {atom, animal, planet, solar system, galaxy, etc}? Can you then use the analysis to predict when the ...
7
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0answers
108 views

Does quark color contribute to “spin degeneracy” for QGP calculations?

Like the title say, does quark color matter in counting contributions in a early universe plasma (QGP), as when adding up the total plasma energy density, or is it just spin? The book I have (Pathria) ...
2
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1answer
565 views

Accessible microstates of harmonic oscillator in microcanonical enemble

While reading up on statistical physics, I am going through the calculation of the partition function of the harmonic oscillator in the microcanonical ensemble. The result for the partition function ...
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1answer
158 views

Uncertainty and Thermodynamics

Dilemma The uncertainty principle of energy and the 2nd law of thermodynamics don't add up : the uncertainty principle of energy says that $\Delta \tau \cdot \Delta E \ge \frac{h}{4\pi} = ...
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1answer
175 views

Maximizing Multiplicity of Einstein Solid == (Temperature = $\infty$)?

If I have a system consisting of 2 Einstein solids (A and B) is it equivalent to say that maximizing the multiplicity of the ...
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0answers
64 views

Increase in number of micro states explanation or restatement of second law?

Is the boltzmann's expression of entropy as log of micro states leading to the formulation that system is more likely to be in a macrostate with more no. Of micro states really is an explanation or ...
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2answers
602 views

Spontaneous conversion of heat into work at negative temperatures

Consider a heavy macroscopic object moving in a gas. Friction causes its kinetic energy to be converted into heat. Thermodynamically, there is (effectively) no entropy associated with the kinetic ...
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2answers
379 views

Energy of particle in electric field

I'm taking a physics class and the professor teaches us really basic things in lecture and then gives homework way beyond what he taught in lecture. Obviously I need to find some resource other than ...
3
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1answer
556 views

Why the chemical potential of massless boson is zero? [duplicate]

In Bose-Einstein condensation, the chemical potential is less than the ground state energy of the system($\mu<\epsilon_g$). But why does the massless boson such as photon have zero chemichal ...
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1answer
506 views

Pauli paramagnetism for electrons with external magnetic field

Apparently it is to be shown that for electrons under an external magnetic field, in the limit as $B\to 0 $ $$ \chi = \frac{dM}{dB} \approx \frac{n\,\mu^{*^2}}{k\,T}\,\frac{f_{1/2}(z)}{f_{3/2}(z)} $$ ...
4
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3answers
801 views

Does entropy really always increase (or stay the same)? [duplicate]

Consider this image. If the big (grey) molecules were all to spontaneously move to the left, and the small ones were to move to the right, there would be an increase in order. While unlikely, ...
2
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1answer
164 views

classical quantum particles in grand canonical ensemble

To derive Bose-Einstein and Fermi-Dirac distribution, we need to apply grand canonical ...
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1answer
576 views

Differences between hard-core boson and fermion

Hard boson has strong repulsion with each other just like fermion. What is the differences between hard-cord boson and fermion. Which materials are hard-core bosons?
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1answer
186 views

Change of variables, Fermi Integral

This is a really basic question, but I'm kind of confused. I have this integral $$\int_{0}^{\infty}\frac{p^{2}dp}{e^{\alpha+\beta p^{2}/2m}+1}$$ where ...
3
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2answers
343 views

What is wrong with these ways of determining the mean occupation number?

Could anyone point out what went wrong in this argument? Setup: We have a system with 2 energy levels say with energies $0,e$ respectively. We consider the grand canonical ensemble for the system ...
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0answers
35 views

Is there anything to prevent paired-up neutrons from a complete overlap

The reason "neutrons don't overlap", as DarenW explained it, has to do with intricate forces at play that take into account the spins, iso-spins and symmetry of the wavefunctions. However, assume I ...
2
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1answer
212 views

Local minima in Ising model in a Monte Carlo simulation

Is there any way to check whether in a Monte Carlo simulation using Ising model is stuck in any (false) local minima of energy or not, particularly in 3D system ?
4
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1answer
942 views

Bohr-van Leeuwen theorem and quantum mechanics

Preamble: If one considers an ideal gas of non interacting charged particles of charge $q$ in a uniform magnetic field $\mathbf{B} = \mathbf{\nabla} \wedge \mathbf{A}$, then the classical partition ...
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1answer
249 views

Math for Thermodynamics Basics

I am studying Statistical Mechanics and Thermodynamics from a book that i am not sure who has written it, because of its cover is not present. There is a section that i can not understand: ...
4
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2answers
427 views

Erogodicity in a Monte Carlo simulation

Q1: What is the ergodicity and ergodicity breaking in a Monte Carlo simulation of a statistical physics problem? Q2: How does one ensure that the ergodicity is maintained ?
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2answers
167 views

Probabilistic vs Statistical interpretation of Double Slit experiment

Why is it assumed that the results seen in the double slit experiment are probabilistic and not just a statistical result of some unknown variable or set of variables within the system.
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1answer
423 views

How to define the order parameter of the q-state Potts model?

The order parameter of Ising model can be defined as $m=\frac{N_1-N_2}{N}$, if $N$ is the total number of lattice points, $N_1$ and $N_2$ is the number of lattice points spin up and down respectively, ...
4
votes
3answers
535 views

Is there a mechanism for time symmetry breaking?

Excluding Thermodynamic's arrow of time, all mathematical descriptions of time are symmetric. We know the arrow of time is real and we know the equations describing physics are real so is there any ...
3
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1answer
483 views

Third-order phase transition in Landau theory

$F=\frac{a}{2}m^2+\frac{u}{4}m^4+\frac{v}{6}m^6-hm$, where F is the free energy, m is the order parameter, h is the external field, $a=a_0(T-T_c)$, and $a_0>0,u>0$ and $v>0$.We know this free ...
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2answers
708 views

Dispersion relation and Heat Capacity

I have seen case studies of the 3D Debye model where the vibrational modes of a solid is taken to be harmonic with dispersion relation $\omega = c_sk$. It is said that for temperatures much less than ...
4
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1answer
156 views

Semi-conductors

Suppose there is a semiconductor with Fermi energy $E_f$ and that there are $N$ bound electron states. I'd like to know why the mean number of excited electrons takes the form $$\bar n={N\over ...
4
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1answer
582 views

Intuition behind classical virial theorem

I am continuing to brush up my statistical physics. I just want to gain a better understanding. I have gone through the derivation of the classical virial theorem once more. I have thought about it, ...
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1answer
117 views

Interacting particles

We are familiar with the grand partition function for the grand canonical ensemble. This makes me wonder: what kinds of modifications would be required if the particles interacted? Thanks.
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1answer
127 views

microcanonical distribution

We know that in an isolated system, the density matrix is the microcanonical distribution matrix. That this the possibility for all the states with energy in a certain interval is a constant? But how ...
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2answers
258 views

Behaviour of individual terms in Einstein-Smoluchowski fluctuation-dissipation relation

Consider a bath of Brownian particles at temperature $T$. If we sprinkle some larger particles in this (eg: pollen grains in water or dust motes in air), they'll diffuse with diffusion constant $D$ ...
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0answers
432 views

Rotational Constant and Moment of Inertia of Fluorine gas

I have come across some homework question on thermodynamics which needs me to calculate $B$ of $F_2$ My attempt: $B= \frac{h}{8\pi^2cI}$ where $I=\mu r^2=\frac{m_1m_2}{m_1+m_2} r^2$ Atomic mass of ...
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0answers
149 views

Deriving the “total” Bose Einstein density of states, including the condensate

Is is possible to derive the Bose-Einstein density of states containing the delta function representing the BE condensate?
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0answers
92 views

Does the Standard Model plasma develop a spontaneous magnetisation at finite temperature?

Reference: arXiv:1204.3604v1 [hep-ph] Long-range magnetic fields in the ground state of the Standard Model plasma. Alexey Boyarsky, Oleg Ruchayskiy, Mikhail Shaposhnikov. The authors of this paper ...
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3answers
351 views

Results of Statistical Mechanics first obtained by formal mathematical methods

I have a question that seems natural in Physics and Mathematics mainly in Statistical Mechanics of Equilibrium. Results that are proven by formal mathematical methods that were already seem intuitive ...
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0answers
210 views

Ground and first excited state of non interacting spin system Hamiltonian

For a non interacting spin system containing two $\frac{1}{2}$ spin particles I am trying to determine its Hamiltonian. If the energy of a up spin is $+\mu {\bf B}$ and a down spin is $-\mu {\bf B}$, ...
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1answer
347 views

Ground states of the Hamiltonian of a two spin system

For the spin system shown in this graph (http://i.stack.imgur.com/3lg1R.png), the Hamiltonian is $$S^{(1)}_z\cdot S^{(1)}_z=\frac{1}{4}\begin{pmatrix} 1 & 0 &0 &0 \\ 0&-1 &0 ...
2
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1answer
134 views

Eigenvalues of a mean correlation matrix (integral over correlation matrices with arbitrary density)

Consider a stationary dynamic system with state $s(t)$ and correlation structure described by $C_{ij}(\tau)=\mathbb{E}[(s_i(t+\tau)-\bar{s_i})(s_j(t)-\bar{s_j})]$. Given an arbitrary density function ...
0
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1answer
531 views

Pure state - density matrix - real life example of boxes in warehouse

So if there are a billion boxes in a warehouse, I would like to know conceptually how to tell if it is in a pure state. I know that if it is in a pure state (not mixed) that the density matrix has ...
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2answers
5k views

The number of degrees of freedom of a monatomic gas

Suppose that I have a monatomic gas sample consisting of $N$ atoms (e.g., $N$ argon atoms); thus there are no vibrations or rotations. How many degrees of freedom does the system have? Does the ...
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1answer
134 views

Hamiltonian of a simple graph

I have a spin system: As shown in the picture, there are two spins S1 and S2, and a pair of interactions between them. One is a ferromagnetic interaction and the other is anti ferromagnetic ...
2
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0answers
206 views

Spontaneous symmetry breaking in the quantum 1D XX model?

The ground states of the quantum 1D Ising and Heisenberg models exhibit spontaneous magnetization. Is this also true for the 1D XX model?
2
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2answers
1k views

Absolute zero and Heisenberg uncertainty principle

I got to read Feynman vol I and there was written that at absolute zero, molecular motion doesn't cease at all, because if so happens, we will be able to make precise determination of position and ...
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1answer
1k views

Significance of the the Lagrange multipliers in statistical mechanics

In classic thermodynamics one can derive the Maxwell Boltzmann statistics by solving a Lagrange multipliers equation. In this process a new parameter $\beta$ is introduced to take account of the total ...
2
votes
3answers
694 views

Why the temperature is getting lower when the universe is expanding

As we know, if an ideal gas expands in vacuum, as its energy is unchanged, the temperature remains the same. An ideal gas's energy does not depend on volume. In general, the energy is $kT$ times the ...
2
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1answer
138 views

Reaction coordinate as a function of atomic positions

I'm going over some (molecular dynamics) related literature - specifically the derivation of the Weighted Histogram Analysis Method (WHAM). As a quick backdrop WHAM is a method for stitching ...
4
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1answer
281 views

Classical blackbody radiation 'solution'

I never understood how the equipartition theorem was applied electromagnetic waves inside the metallic blackbody. As hyperphysics puts it ...
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2answers
805 views

Is there a formal definition of a macroscopic variable in statistical mechanics?

Intuitively it's easy to accept that the usual variables like temperature, internal energy, etc. are 'macroscopic', but does there exist a formal definition of a macroscopic variable? In other ...
5
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2answers
414 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 ...
3
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2answers
684 views

Canonical partition of a boson gas

I have a 1D gas made of $N$ particles placed in a harmonic potential well, so the Hamiltonian is: $$ \mathcal H = \sum_{j=1}^N \left ( \frac{p_j^2}{2m} + \frac{1}{2}m\omega^2 x_j^2 \right )$$ The ...
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0answers
76 views

Partition function for multidimensional scaling energy

Let $D_{ij}$ a random matrix with i.i.d positive coefficients. One can take for instance $D_{ij}$ uniformly distributed in [0,1]. We consider the following energy function $H(x)$ defined for ...