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

learn more… | top users | synonyms

0
votes
0answers
19 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: ...
2
votes
1answer
31 views

How does low entropy in the distant past translate into the observed entropy increases?

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 ...
1
vote
1answer
37 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 ...
1
vote
0answers
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 ...
1
vote
0answers
77 views

Diamagnetism of a degenerate electron gas for weak fields

In the book "Statistical Physics, Part I ($3^{{\rm rd}}$ edition)" by Landau and Lifshitz, at $\S59$ when he treats the diamagnetic part of the magnetisation of a degenerate electron gas for weak ...
2
votes
0answers
38 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 ...
0
votes
1answer
73 views

Canonical ensemble, energy, heat bath

I am studying through the book Thermodynamics and Statistical Mechanics by Walter Greiner and I’ve got a couple of doubts when I was reading about the classical ensembles, specially the Canonical ...
0
votes
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 ...
0
votes
0answers
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 ...
4
votes
3answers
265 views

Existence of negative temperatures and the definition of entropy

How negative temperatures can be possible has been treated on StackExchange before (several times in fact), but in light of some recent academic discussion, most of these answers seem to be possibly ...
1
vote
4answers
68 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 ...
10
votes
1answer
494 views

Why is (von Neumann) entropy maximized for an ensemble in thermal equilibrium?

Consider a quantum system in thermal equilibrium with a heat bath. In determining the density operator of the system, the usual procedure is to maximize the von Neumann entropy subject to the ...
3
votes
2answers
73 views

What materials are used in non thermal plasma?

While reading about non-thermal plasmas, I came across their ionization potentials(~1%), and other capabilities, such as their non Maxwellian energy distributions. At what temperatures, and pressures ...
5
votes
2answers
1k views

Hit a bottle of beer on the top with another causes the first to spit all the gas, why?

So, on the other day me and my colleges were discussing the following phenomena: Pick two open bottles of beer. With the bottom of the first, hit the second on the bottleneck, in the following way: ...
3
votes
3answers
98 views

Statistical Mechanics - Distribution of Energies

Consider a state space $\mathbb{X}$. The probability density function under a canonical ensemble is given by the Boltzmann distribution $$\pi_{\mathbb{X}}(x)=\frac{e^{-\beta ...
0
votes
0answers
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.
0
votes
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?
0
votes
0answers
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 ...
2
votes
1answer
76 views

error propagation and collision in ideal gas

When dealing with gas, a statistical approach is needed because For N particles, you have to solve 6N equations which cant be done analytically. To know our time step for numerical solving, you can ...
2
votes
3answers
240 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
106 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 $$ ...
1
vote
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 ...
0
votes
1answer
80 views

Difference between heat and work

According to the Kinetic Theory of Matter, temperature is nothing but a measure of the kinetic energy of matter. My textbook says that the change in internal energy of a system is the heat gained plus ...
0
votes
0answers
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 ...
0
votes
0answers
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 ...
1
vote
1answer
63 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 ...
1
vote
2answers
319 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 ...
0
votes
0answers
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 ...
0
votes
0answers
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 ...
0
votes
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 ...
0
votes
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 ...
3
votes
4answers
176 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
votes
1answer
207 views

How to derive the two-term approximation for the Boltzmann equation?

Starting with the Boltzmann equation in terms of $f(t,\vec v,\vec x)$ or $f(t,\vec v)$ http://en.wikipedia.org/wiki/Boltzmann_equation $$\left(\frac{\partial}{\partial t} + \vec{v} \, ...
1
vote
1answer
43 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 ...
16
votes
1answer
172 views

Fluctuations of an interface with hammock potential

This question is related to that one. I ask it here since comments are too short for the extended discussion that was going on there. I am interested in a very simple interface model. To each ...
1
vote
1answer
45 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 ...
5
votes
2answers
103 views

How can the microstates be measured with zero energy expenditure?

James P. Sethna. Statistical Mechanics. Exercise 5.2: What prevents a Maxwellian demon from using an atom in an unknown state to extract work? The demon must first measure which side of the ...
0
votes
0answers
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. ...
0
votes
1answer
183 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 ...
0
votes
0answers
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 ...
1
vote
0answers
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 ...
2
votes
3answers
471 views

What are thermal energy distributions?

I am trying to understand the photoelectric-effect deeply. My teacher used the Planck's law and integrated it to deduce the Stefan-Boltzmann law. He somehow showed some quantum-physical ...
0
votes
0answers
43 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 ...
11
votes
2answers
249 views

Proof of Loss of Lorentz Invariance in Finite Temperature Quantum Field Theory

In the standard quantum field theory we always take the vacuum to be a invariant under Lorentz transformation. For simple cases, at least for free fields, is very simple to actually prove this. Now ...
0
votes
1answer
116 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 ...
0
votes
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 ...
0
votes
1answer
82 views

What does the behavior of the pair correlation function look like in the vicinity of the critical point?

What does the g(r) look like near the critical point? I know what the pair correlation function (radial distribution function) should look like for a solid, which has regular packing and therefore ...
1
vote
0answers
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 ...
1
vote
0answers
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 ...
4
votes
0answers
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 ...