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

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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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21 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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36 views

Calculate Helmholtz Free Energy with Entropy, Work given [on hold]

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 ...
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2answers
17 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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2answers
29 views

Derivation of ensemble distribution

I heard that you can derive the canonical ensemble by maximizing $L = \sum_i p_ilog( p_i ) + \alpha (\sum_i p_iE_i-E)$ or for the grand-canonical ensemble $L = \sum_i p_ilog( p_i ) + \alpha ...
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1answer
28 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 ...
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20 views

Examples of systems with linear response behavior

I've checking the linear response theory and there are 3 fundamental assumptions. 1) Linearity of the response of the system to an external excitation, 2) Stationary response function: ...
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1answer
48 views

How does the second law of thermodynamics follow from low entropy of early universe?

One of the explanations of the second law of thermodynamics is that it goes back to the low entropy in the early universe (How do you prove the second law of thermodynamics from statistical ...
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1answer
40 views

Equivalent tensor order parameters of nematic liquid crystals?

I found in the literatures two different definitions of the tensor order parameter of nematic liquid crystals. One is $$ Q_{ij}=\frac{S}{2}(3n_{i}n_{j}-\delta_{ij}), $$ where $S$ is the scalar order ...
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40 views

How did Rayleigh and Jeans apply the Equipartition of Energy in determining the energy distribution of blackbody - radiation? [duplicate]

I am reading the Ultraviolet Catastrophe and have come across this law. Here , it is written They applied the statistical physics method to the waves by analogy with Maxwell's gas particles using ...
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0answers
41 views

Relationship between Liouvile's theorem and Diffusion equation

Consider a Hamiltonian system. According to the Liouville's theorem there exists a probability density function $\rho(q^a,p_a,t)$ in the phase space whose evolution is given by $$ \frac{\partial \rho ...
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24 views

Mean square velocity of an ideal Bose gas

I'm trying to find the mean square velocity of a particle in an ideal Bose gas. The equation is given by: $\langle v^2 \rangle = \dfrac{1}{N}\displaystyle\sum_{\vec{k}}(\hbar ...
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8 views

How is the pattern of the decay of cluster expansion coefficient

For cluster expansion applied in material prediction. Is there some general trends how the ECIs should decay? Thank you.
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1answer
38 views

Defintion of temperature without thermal equilibrium condition

Is temperature only defined in thermal equilibrium? Then how can we explain heat flow by temperature differences?
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4answers
69 views

Statistical physics and momentum conservation

In statistical physics one usually looks at energy as a conserved quantity and e.g. in the canonical ensemble assumes a constant average energy of the ensemble. Now why don't we usually do this for ...
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1answer
20 views

Relation between Curie temperature and exchange interaction's constant $J_\text{ex}$

I'm running a Monte Carlo simulation on a generic magnetic nanotube. In my results, I found out that the relation between the Curie temperature (that is, the temperature by which a ferromagnetic ...
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16 views

Ising Monte-Carlo and Three point functions

I'm looking for literature on the calculation of three points function in the 2d Ising Model using numerical methods, especially around the critical point. By $Z_2$ symmetry, three spin insertions is ...
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0answers
47 views

Interpretation of partition function and thermodynamic potential

So in the microcanonical ensemble the partition function $\Omega$ counts the number of microstates for a given $(NVE)$ configuaration and $S = k_B \ln (\Omega)$ is the entropy. The most likely state ...
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27 views

Is entropy related to Poincare recurrence time?

One of the ideas involved in the concept of entropy is that nature tends from order to disorder in isolated systems. But we even know that Poincare recurrence time also is a particular time after ...
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15 views

Many body quantum rotors

I'm stuck on a particular problem about quantum rotors. Suppose we have $N$ such rotors and they are connected to a thermal reservoir of temperature $T$. Neglecting any center of mass motion, I'm ...
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1answer
65 views

Maxwell-Boltzmann distribution - find error in derivation

I have a derivation of the Maxwell-Boltzmann distribution: Consider a gas consisting of only one type of molecules, which is in an equilibrium with a heat reservoire of temperature T. Since ...
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26 views

Need a simple derivation for Stat Mech [migrated]

I actually know the formula for this which is $\frac{N!}{n_{1}!n_{2}!}$ ,but need some help to derive this. Find the number of distinct ways of arranging N particles in two groups such that one group ...
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0answers
18 views

Coupling a ferromagnet to an antiferromagnet

Consider a system composed of a thin film of FM material on top of an AFM material. From my research I found that pinning of the FM material occurs when we cool the system from $T_N<T<T_C$ to ...
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1answer
74 views

Do physicists use agent based models?

I am hoping that this is a simple and specific question. I just wanted to know whether physicists from any branch of physics use agent based models as a tool in their research? If so, then in which ...
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24 views

Chemical potential related with quantum and classical limit in ideal gas

For ideal gas we have chemical potential $\mu = \tau \ln \left(\frac{n}{n_Q}\right) $ where $n = N/V$ number density and $n_Q = \left(\frac{M\tau}{2\pi \hbar^2}\right)^{\frac{3}{2}} $ Note we call ...
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17 views

Pressure components in a film

I am performing molecular-dynamics simulations of a polymer near a crystalline substrate (polymer film). I am comparing the mechanical properties in the film with the properties in the bulk polymer. ...
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30 views

The relationship between the two statistical mechanical definitions of entropy

It seems like similar questions have been asked here; hopefully my question is not a duplicate. I am reading my textbook on the statistical mechanical definitions of entropy, and I am very confused ...
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30 views

classical and quantum correlation functions

Quantum Field, quantum fluctuation even with no temperature In QFT, the correlation function $<0|\hat{\phi} (x)\hat{\phi} (y)|0>$ describes the fluctuation correlations of vacuum state ...
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44 views

Partition function microcanonical ensemble

I was wondering if there is a way to understand the partition function for a microcanonical ensemble $$\mathcal Z(E)=\sum_{\text{microstate $i$ with energy $E$}} w_i$$ as a limit of the continuous ...
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1answer
17 views

Help Understanding Correlations In Many Particle (Beam) Physics

I am having a lot of trouble looking at the statistical properties and having some sort of intuitive sense of correlations among different properties of many body systems (in particular charged ion ...
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20 views

Bose Enhancement Factor

How may one explain the fact that the probability of a boson transferring to a state with an occupation number n is 'enhanced' by a factor of (1+n), compared to the classical case? (In the classical ...
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13 views

General Gaussian distribution relation [migrated]

I'm trying to solve a question from Pathria's statistical mechanics textbook (10.21). Show that, for a general Gaussian distribution of variables $u_j$ , the average of the exponential of a linear ...
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0answers
45 views

Reduced phase space density

I have a dimensional problem with the single particle phase space density The partition function in the microcanonical ensemble is of course dimensionless Thus $$ \rho ( q, p ) = ...
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67 views

References to Mechanics (Classical, Quantum, Statistical) using Time-Scale calculus?

Time-Scale Calculus, is a theory which unifies ordinary (plus fractional and q-) calculus with discrete (and finite differences) calculus. In a sense, in a similar way the Lebesgue integral (or ...
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1answer
41 views

How to prove $f_1f_2 \rightarrow f_1f_2(1\pm f_3)(1\pm f_4) $ in Boltzmann equation of degenerate gas?

How to prove $f_1f_2 \rightarrow f_1f_2(1\pm f_3)(1\pm f_4) $ in Boltzmann equation of degenerate gas ? I know it's Bose enhancement and Fermi block. I want to know why it's exactly this form? For a ...
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1answer
92 views

Doesn't entropy increase backwards in time, too?

In statistical explanations of entropy, we can often read about a (thought) experiment of the following sort. We have a bunch of particles in box, packed densely in one of the corners. We assume some ...
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1answer
117 views

Ideal gas in ensemble

I want to calculate the phase space density for a single ideal gas particle in a microcanonical ensemble. I know that the partition function is given by the well-known expression that you find for ...
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2answers
31 views

Entropy of ideal gas with finite volume

I know that the entropy of an ideal gas is given by the Sackur-Tetrode equation, but is there also a way to take into account that even the ideal gas will acquire some volume $v_0$? Or is it then just ...
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1answer
29 views

Applications of statistical mechanics [duplicate]

I'm trying to learn statistical mechanics on my own. I'm reading about canonical and grand canonical ensemble and I'm making good progress. The problem is that I can't find interesting applications of ...
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2answers
61 views

Partition function containing QM?

I am wondering about the partition function of the classical microcanonical ensemble. It contains Planck's constant and also an indistinguishability argument about the particles I am looking at and I ...
4
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2answers
99 views

What is the connection between the non-reversibility of the decay of unstable nuclei (as Uranium, Plutonium) and the 2nd principle of thermodynamics?

The 2nd principle of the thermodynamics says that if a system (e.g. an ideal gas) is left undisturbed, its number of microscopic states only increases. This is a statement of irreversibility of the ...
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2answers
75 views

Second Law from Statistics

Hi all I hope you can help me with the statistical origins of the Second Law. I cannot find anything that mathematically proves that order from disorder is impossible only improbable Leading me to ...
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1answer
44 views

In statistical mechanics, what does integrating with respect to the position of a molecule mean?

So, this is probably a dumb question, but I cannot visualize or make sense of integrating over the position of a molecule in space. Okay, so an example in my thermodynamics textbook: we have N = 5 ...
2
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1answer
55 views

Equilibrium in Stat Mech and Phase space density

I was wondering if there is any relationship between equilibrium in Stat Mechanics and the phase space density of a system? This does not seem to be completely independent, as Entropy is maximized in ...
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0answers
55 views

Statistics of many body systems in pure states

My understanding of describing a system in thermal equilibrium is that we introduce an ideal thermal reservoir for convenience and then imagine that the system+reservoir samples all states of constant ...
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42 views

Meaning of phase space density

I am trying to understand Liouville's theorem physically. It says that $\frac{\partial \rho}{\partial t} + \{\rho,H\} = 0$. Thus, we have $\frac{d \rho(q(t),p(t),t)}{dt}=0$. I would like to ...
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14 views

Distribution and different ways of distribution

Is "the number of ways of of distributing $N$ things across a fixed set of energy levels the same as "the number of ways a particular distribution can be realised? My book seems to say that $W$ is ...
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0answers
28 views

Boltzmann factor predicts arbitrarily large numbers of electrons at high potential?

In deriving the Debye shielding length we are told that the Boltzmann factor for particles of charge $q$ is: $n_{q}=n_{0}\exp(-q\phi/kT)$ If we assume the potential $\phi$ is positive, then the ...
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20 views

Screened potential of charged impurity in a 2-dimentional electron gas

What's the analytical relation of screened potential of charged impurity in a 2-dimentional electron gas?
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64 views

Boltzmann distribution - statistical mechanics

I have just followed a derivation of the Boltzmann distribution which I have never seen before, and I must say it is really intuitive. However I have a question as to how we can think of the Boltzmann ...