The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.
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1answer
51 views
+100
Leap from photon gas energy distribution to black body radiation?
I remember considering in class in college, the case of a photon gas trapped in a d-dimensional box as a subject of interest, whose energy distribution, heat capacity, etc. should be calculated.
...
2
votes
0answers
42 views
Evolution of black holes ensemble
If the Universe contained only black holes with a certain mass and velocity distribution, how would it evolve over time? Is it enough to know the mass/velocity distribution to predict the general ...
1
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1answer
43 views
How to derive the expression for Bose-Einstein distribution variance?
Can anyone point me to a derivation of this expression? $n_s$ is the number of bosons in a state.
1
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0answers
32 views
Maxwell-Boltzmann distribution
The short story is, that I have to calculate some transport coefficients, but using the the MB distribution as my distribution function.
What I currently need to solve is:
${{\mathcal{L}}^{\,\left( ...
5
votes
4answers
151 views
Can a single molecule have a temperature?
A show on the weather channel said that as a water molecule ascends in the atmosphere it cools. Does it make sense to talk about the temperature of a single molecule?
1
vote
1answer
183 views
Simulating quantum network of harmonic oscillators
Let's say that I have a system of $n$ particles $p_1,\ldots,p_n\in\mathbb{R}^3$ (where $n$ here is on the order of 10,000). Furthermore, suppose we have a graph $G=(V,E)$ describing some network, ...
0
votes
1answer
50 views
From Fermi-Dirac to Maxwell-Boltzmann statistics
I have a little question I can't seem to find the answer to. It is as follows:
When does Fermi-Dirac statistics reduce to Maxwell-Boltzmann statistics?
6
votes
1answer
87 views
Precise statement of Mermin–Wagner theorem
Roughly speaking, Mermin-Wagner theorem states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions ...
3
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0answers
39 views
How long would it take for a container in vacuum to leak half of its air?
Let's say I know the size of the container, size of the hole the air leaks through, pressure the air is under and temperature of the air if that helps anything. Is it possible to calculate this only ...
6
votes
1answer
65 views
Dependence of chemical potential to zero point of energy
The chemical potential is defined as:
$$
\mu = -T\frac{\partial{S(N,V,E)}}{\partial{N}}
$$
It seems to me that this is completely independent of where I put the reference point of energy, because only ...
2
votes
0answers
29 views
Relevant operators in two dimensional O(n) models
The most general hamiltonian of a two dimensional $O(n)$ and $Z_2$ invariant statistical model can be written:
$$
H=\int d^2 x \left[\frac{\nabla \mathbf{\phi}^2}{2} + \frac{m_0^2}{2}\mathbf{\phi}^2 ...
1
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1answer
43 views
Sackur-Tetrode equation - clarification required - problem with units
I'm a 2nd year physics undergraduate and recently I've volunteered to give a short presentation on the Sackur-Tetrode equation derivation and its use at removing the Gibbs paradox. I've looked on the ...
2
votes
2answers
120 views
Why is the temperature zero in the ground state?
This is probably a simple question: I see this claims in many books, but I can't figure a reason why this is true.
So my question is why this claim is true:
"If we know that the system is in the ...
2
votes
3answers
81 views
Question about the proof that heat capacity goes to zero if temperature approaches $0K$
I don't completely understand the proof that is given for the claim that the heat capacity goes to zero, if the temperature approaches $0K$.
They do it as follows, if $C_x$ is the heat capacity where ...
2
votes
3answers
125 views
What is the general statistical definition of temperature?
Temperature in an isolated system is defined as:
$$\frac{1}{T} = -\frac{\partial{S(E,V,N)}}{\partial{E}} $$
But I wonder how one can generalize this to a random system.
Or for instance to a point in ...
1
vote
1answer
67 views
Basic energy calculation for N identical spin system
We have a system that has N identical spins $n_i$, and each spin can be in state 1 or 0. The overall energy for the system is $\epsilon\sum_{i=1}^{N}n_i$.
My understanding: There is only one ...
3
votes
0answers
46 views
Lattice model completely constrained by boundary data
I am dealing with a lattice model that has the peculiar property that if I specify all the spins on the boundary, by local conservation laws, the whole lattice configuration (throughout the whole ...
0
votes
0answers
53 views
Why does the cross derivative of the partition function disappear here?
They state that the chemical potential in a canonical ensemble is given by:
$$\mu = -kT \frac{\partial{\ln Z(N,V,T)}}{\partial{N}} \tag{1}$$
But if I use the definition of chemical partial (which I ...
0
votes
0answers
26 views
Existence of Boltzmann Distribution With Constraints [closed]
I have a problem with showing the existence of Boltzmann distribution given some constraints.
Consider $p_1,...,p_n$ a Boltzmann distibution, where $p_i=\frac{\epsilon^{-\beta \cdot E_i}}{\sum_{j}^{} ...
2
votes
2answers
70 views
Error in variance
I've been exploring techniques in statistical physics, specifically applying them to spin ices. I'm in the canonical ensemble. By using the fluctuation dissipation theorem you can extract useful ...
1
vote
1answer
62 views
Question about the Boltzmann distribution
In the derivation of the Boltzmann distribution they consider a system $A$, enclosed by a diathermal wall in a heat reservoir $R$. Then they calculate the probability that the system $A$ is in an ...
0
votes
0answers
29 views
Maxwell-Boltzmann distribution for transport equations
I have to calculate the transport coefficients for the Maxwell-Boltzmann distribution. But I'm not sure what distribution I have to use.
As far as I know it should not be the MB distribution for ...
1
vote
1answer
141 views
Occupied lattice sites, determining number of microstates and energy
A solid consisting of $N$ molecules on a lattice of $N$ sites is isolated from its environment, and has energy $E$. Each molecule is fixed in position and independent of all others. It can be in any ...
1
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1answer
63 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 ...
1
vote
2answers
65 views
Energy dependent Maxwell-Boltzmann distribution
I'm having a bit of a problem figuring out the energy dependent Maxwell-Boltzmann distribution.
According to my book (Ashcroft & Mermin) they write the velocity dependent distribution as:
...
4
votes
3answers
180 views
Definition of entropy
In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) entropy of a variable $X$ is ...
2
votes
1answer
63 views
NP-completeness of non-planar Ising model versus polynomial time eigenvalue algorithms
From the papers by Barahona and Istrail I understand that a combinatorial approach is followed to prove the NP-completeness of non-planar Ising models. Basic idea is non-planarity here. On the other ...
0
votes
1answer
217 views
How much energy Maxwell's demon will earn?
Suppose we have one mole of one-atom ideal gas at temperature $T$.
Suppose Maxwell's daemon has separated molecules into two sections, one with speed below mean and another with speed above mean.
...
2
votes
2answers
57 views
What is the derivation for the exponential energy relation and where does it apply?
Very often when people state a relaxation time $\tau_\text{kin-kin}, \tau_\text{rot-kin}$,, etc. they think of a context where the energy relaxation goes as $\propto\text e^{-t/\tau}$. Related is an ...
4
votes
2answers
89 views
What would happen if energy was conserved but phase space volume wasn't? (and vice-versa)
I'm trying to understand the relationship between the two conservation laws. As I understand, Liouville's result is a weaker condition: it relies merely on the particular form assumed by Hamilton's ...
2
votes
3answers
421 views
Does high entropy means low symmetry?
According to Bogolubov postulate (various texts name it differently) in Non-equilibrium thermodynamics, the number of needed parameters to describe our system is decreasing with time, and finally at ...
2
votes
0answers
41 views
What is the minimum non-integer dimension for which the XY model shows a phase transition? (if well-defined)
I know that XY statistical model for $d=2$ doesn't show a regular phase transition , while the $3d$ has, I was wondering what is the behaviour for $2< d < 3$.
If it is simpler one could ...
3
votes
2answers
280 views
Can a first order phase transition have an order parameter?
Order parameter is used to describe second order phase transition. It seems that in some papers it is used in the first order phase transitions. Can first order phase transition have an order ...
8
votes
3answers
206 views
comments on entropy and direction of time in Landau and Lifshitz stat mech
In Landau and Lifshitz's Stat Mech Volume I is the comment:
Thus in quantum mechanics there is a physical non-equivalence of the two diretions of time, and theoretically the law of increase of ...
6
votes
1answer
76 views
Motivation for the Deformed Nekrasov Partition Function
I have recently been doing research on the AGT Correspondence between the Nekrasov Instanton Partition Function and Louiville Conformal Blocks (http://arxiv.org/abs/0906.3219). When looking at the ...
1
vote
1answer
68 views
What is the interface tension between ordered and disordered phases of the Potts model?
I read in these papers(1,2) the concept of interface tension. I can't understand its definition. I can hardly imagine there is some tension in a model. Any help will be appreciated.
1
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4answers
86 views
The Preference for Low Energy States
The idea that systems will achieve the lowest energy state they can because they are more "stable" is clear enough. My question is, what causes this tendency? I've researched the question and been ...
2
votes
0answers
66 views
Ising Hamiltonian for relativistic particles
An Ising system is described by the simple Hamiltonian:
$$H = \sum\limits_{i} c_{1i} x_{i} + \sum\limits_{i,j} c_{2ij} x_i x_j \,\,\,\,\,\,\,\,\,\,(1)$$
Here the $x_i$ are spins (+1 or -1 in units ...
3
votes
4answers
209 views
If particles can find themselves spontaneously arranged, isn't entropy actually decreasing?
Take a box of gas particles. At $t = 0$, the distribution of particles is homogeneous. There is a small probability that at $t = 1$, all particles go to the left side of the box. In this case, entropy ...
9
votes
3answers
252 views
Is there a way to obtain the classical partition function from the quantum partition function in the limit $h \rightarrow 0$?
One would like to motivate the classical partition function in the following way: in the limit that the spacing between the energies (generally on the order of $h$) becomes small relative to the ...
20
votes
4answers
749 views
Is there a Lagrangian formulation of statistical mechanics?
In statistical mechanics, we usually think in terms of the Hamiltonian formalism. At a particular time $t$, the system is in a particular state, where "state" means the generalised coordinates and ...
0
votes
1answer
215 views
Expressions for canonical partition function and probabilities $p(E_i)$
Given an atom with 4 allowed states corresponding to the energy levels
$E_1 = 0$, $E_2 = E$, and $E_3 = 2E$ with degeneracies 1, 1, and 2 respectively.
How do I find the expressions for the ...
0
votes
3answers
1k views
What is a microstate, macrostate and thermodynamic probability in statistical mechanics?
Currently I am learning Maxwells Boltsmann distribution (MBD) and in that I am learning about microstate, macrostate and thermodynamic probability (TDP). I understood the derivation of MBD but I am ...
3
votes
1answer
117 views
How is the dynamic equilibrium nature of fermi-dirac distribution of particles facilitated?
I read this in Kittel: Introduction to Solid State Physics about deriving that product of electron and hole concentration as independent at a given temperature by the law of mass action.
For this ...
6
votes
5answers
466 views
General relativity and the microscopic/macroscopic distinction
Here is Wikipedia's diagram of the stress-energy tensor in general relativity:
I notice that all of its elements are what would be termed "macroscopic" quantities in thermodynamics. That is, in ...
3
votes
1answer
128 views
Phase space in quantum mechanics and Heisenberg uncertainty principle
In my book about quantum mechanics they give a derivation that for one particle an area of $h$ in $2D$ phase space contains exactly one quantum mechanical state.
In my book about statistical physics ...
6
votes
6answers
630 views
Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution?
Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution?
I have never seen dissipation explained, although what I have seen a lot is descriptions of ...
2
votes
1answer
41 views
Temperature of a small system
What is wrong if I define temperature of a small system (I mean, a system which has not a large number of particles) by
$$1/T = dS/dE$$
?
4
votes
2answers
86 views
Independent systems and Lagrangians
Definition 1:
The notion of independent systems has a precise meaning in probabilities. It states that the (joint) probability or finding the system ($S_1S_2$) in the configuration ($C_1C_2$) is ...
1
vote
3answers
75 views
Microscopic picture of an inductor
I have a good understanding of how inductors behave in electrical circuits, and a somewhat rough-and-ready understanding of how this behaviour arises from Maxwell's equations. However, what I don't ...
