# Tagged Questions

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

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114 views

### Chandrasekhar Limit [closed]

A white dwarf is essentially a degenerate electron gas, in which pressure of degenerate electrons supports gravitational pressure. As a simplified model of such an object, consider a spherical star of ...
1answer
84 views

### What is a 'height field'?

I encountered a few times the expression of 'height fields' in statistical physics, without ever reading a proper definition. My textbooks don't seem to talk about that, and googling it hasn't been ...
0answers
81 views

### Free energy a continuous function of temperature but may not be differentiable everywhere?

So according to my understanding, the free energy of the system should be a continuous function of temperature. This is because if the free energy is not continuous at temperature T, then at this ...
1answer
532 views

### Does the Bohr van Leeuwen Theorem also apply to ferromagnetism?

I know that the Bohr-van Leeuwen theorem shows that there could be not consistent pure classical explanation of dia- and paramagnetism. Does the same theorem also rule out a consistent classical ...
0answers
368 views

### Duality between Euclidean time and finite temperature, QFT and quantum gravity, and AdS/CFT

The thoughts below have occurred to me, several years ago (since 200x), again and again, since I learn quantum field theory(QFT) and statistical mechanics, and later AdS/CFT. It is about the duality ...
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168 views

### Fluctuation spectrum of lipid bilayer membranes

I am interestend in calculating the fluctuation spectrum of a thermally fluctuating 2d membane which is only subject to a surface tension $\sigma$. ($\mathcal{H}=\sigma\int\mathrm{d}A$) Depending in ...
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78 views

### Is there a reasonable lower bound for free energy per site of the 2D Ising model in the presence of an external field?

Given the standard Ising partition function: $$Z(\theta ,h) = \sum\limits_{\bf{x}} {\exp \left\{ {\theta \sum\limits_{(i,j) \in E} {{x_i}{x_j}} + h\sum\limits_{i \in V} {{x_i}} } \right\}},$$ is ...
1answer
156 views

### Cluster Expansion vs Cluster Decomposition

Are the cluster expansion (which we encounter in Statistical Physics), and cluster decomposition (in Quantum Field Theory) related to each other? (I have a reason to believe they are)
1answer
198 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 ...
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356 views

### Moments of a Distribution via Laplace Transforms and Wick Rotations [closed]

On a mathematical level, the statistical mechanical partition function is just a Laplace transform of the microcanonical probability distribution, i.e. it's moment generating function. Understanding ...
2answers
106 views

### Can one stimulate emission of a photon with an energy different from the emitted photon?

Suppose I have a three-level system with $E_0$ the ground level, $E_1$ the intermediate and $E_2$ the upper level. In thermal equilibrium they will have a certain probability distribution according to ...
1answer
3k views

### Understanding the mean square displacement in molecular dynamics

In a Molecular Dynamics (MD) simulation, the mean square displacement $\text{MSD}$ is given by $$\text{MSD}(\delta t) = \left\langle\left|\vec{r}(\delta t)-\vec{r}(0)\right|^2\right\rangle,$$ where ...
4answers
909 views

### Question on entropy

All of my textbooks mention, that entropy-change of all spontaneous physical, and chemical processes is positive, and that such processes need another condition to fulfill- decrease in the net ...
7answers
1k views

### Mathematically possible vs physically probable outcomes

A good buddy of mine and I have had a friendly debate about the origins of the current state of our universe (namely; Earth and life on Earth) and have fundamentally disagreed in our stances with ...
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175 views

### Effusion of particles from one box to another - pressure calculation

Suppose we have a container divided into equal halves. Right half is fixed at temperature $T$, volume $\frac{V}{2}$. Initially it has pressure $P_0$, a hole of area $A$ is opened between them. I ...
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61 views

### Can statistical mechanics be formulated generally in terms of phase space?

In many statistical mechanics books, notably Landau and Lifschitz' volume in the course on theoretical physics, the quantities central to statistical mechanics such as entropy are defined in terms of ...
0answers
140 views

### Connection between String theory and Statistical Physics

I would like to think via standard transitivity arguments that there should be a deep connection between String theory and Statistical Physics. Why? Statistical Physics $\rightarrow$ QFT 2d QFT ...
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175 views

### Mean-field theory : variational approach versus self-consistency

I have a general question concerning mean-field approaches for condensed matter classical of quantum statistical mechanic systems. Does determining the mean-field by a variational approach always ...
1answer
66 views

### state on quantum statistics. 3 particles according to 3 distributions [closed]

consider a system of three identical particles, A B ,and C. Assume that each particle can be in one of three possible quantum states, 1,2 and 3. For the following statistics listed below, enumerate ...
3answers
1k views

### What would be non-ergodic physics processes?

As the title says, what would be non-ergodic processes that occur in statistical physics? Many textbooks do not really cover ergodicity really well so I ask this question. I can't suddenly remember ...
2answers
102 views

### Nontrivial critical exponents in exactly solvable models?

Are there any exactly solvable models in statistical mechanics that are known to have critical exponents different from those in mean-field theory, apart from the two-dimensional Ising model? I wonder ...
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121 views

### Wilson's Renormalization Group and Lie's Third Theorem

If you think of a one-parameter group of transformations along a curve in the plane as a (Lie) group, and the tangent vector to the curve as a generator of the curve we can intuitively understand ...
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246 views

### Calculating heat capacity from the equation of state

It is known that within thermodynamics alone, given the equation of the state of a system, one cannot explicitly determine the heat capacity. What is the mathematical reason for this? Intuitively, it ...
0answers
120 views

### Derivation of Higher-order correlation functions from definition

I'm trying to understand the definition of the n-th order correlation function. My aim is to translate the math into a numerical implementation in order to compute the correlation function $g^{(n)}$ ...
1answer
69 views

### Calculation of the differential of the entropy

In this review (for those who wants a precise reference see page 8 eq 21), the Author says that: \begin{equation*} S=-\sum_{i}P\left(i\right)\ln P\left(i\right) \end{equation*} and using the ...
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21 views

### Coarse-graining on a second channel decreases mutual information?

Let $X_1,B_1,X_2,B_2$ and $Y_1,A_1,Y_2,A_2$ and $C_1$ and $C_2$ be binary random variables. Suppose: $I(X_2:B_2|C_2=0)+I(Y_2:A_2|C_2=1) \leq 1$. This can be thought of as a bound on the capacity ...
1answer
318 views

### Entropy is constant. How to express this equation in terms of pressure and density?

In hydrodynamics of an ideal, non-compressive flow we use 5 variables: pressure $p$, density $\rho$ and velocity field $\mathbf{v}$. So we need 5 equations. Landau's "Hydrodynamics" states that the ...
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144 views

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### Classical and Semi-classical treatments of the ideal gas

In the semi-classical treatment of the ideal gas, we write the partition function for the system as $$Z = \frac{Z(1)^N}{N!}$$ where $Z(1)$ is the single particle partition function and $N$ is the ...
2answers
1k views

### Grand canonical partition functions for Bose-Einstein statistics vs. Maxwell-Boltzmann statistics

In Bose-Einstein statistics, the grand canonical partition function is $$\mathcal{Z}=1+e^{-\beta(\epsilon-\mu)}+e^{-2\beta(\epsilon-\mu)}+e^{-3\beta(\epsilon-\mu)}+\cdots$$ In Maxwell-Boltzmann ...
1answer
354 views

### Why are there gapless excitations in the anti-ferromagnetic Heisenberg model while the true ground state is a singlet?

The true ground state of the anti ferromagnetic quantum Heisenberg Model (nearest neighbor only)is known to be a singlet (I think this is Liebs theorem.) Since a singlet is invariant under rotations, ...
1answer
456 views

### I'm getting weird autocorrelations when simulating an Ising model below the critical temperature

So I'm simulating an Ising model using Monte Carlo and the Metropolis algorithm. After letting it reach equilibrium, I try to calculate the autocorrelation of the magnetization. As long as the system ...
1answer
111 views

### Intuitively, why does removing solutes cost $k_B T$ of free energy per molecule?

I can calculate that if you want to, for example, desalinate water, you will have to pay a free energy cost of $k_B T$ for each ion you remove. In other words, removing an ion from a volume of water ...