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

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Spin Glass Transitions in Random Bond Ising Model (RBIM)

In brief, is there a list of spin glass transition properties for the RBIM on different lattices? Is there any know results about the relationships between these probabilities for a graph and its ...
2
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1answer
518 views

Maxwell-Boltzmann velocity PDF to CDF [closed]

I asked on Math.SE and was advised to try here instead. I need to draw from a Maxwell-Boltzmann velocity distribution to initialise a molecular dynamics simulation. I have the PDF but I'm having ...
2
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1answer
456 views

ultrarelativistic gas

Consider the ideal ultrarelativistic gas Hamiltonian $\mathbf{H = }\sum_{i = 1}^N \mathbf{c |\vec{p_{i}}|}$, now if we let molecules to interact with a potential term like $\mathbf{d|\vec{q_{i}}|}$; ...
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4answers
409 views

Comments on entropy and the direction of time in Landau and Lifshitz's Statistical Mechanics

In Landau and Lifshitz's Stat Mech Volume I is the comment: However, despite this symmetry, quantum mechanics does in fact involve an important non-equivalence of the two directions of time. ...
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2answers
2k views

Molecular Dynamics (MD) Simulation: energy fluctuations in NVE ensemble

I'm writing my first MD simulation (ever) for liquid Argon. The code is up and running. I am supposed to do the calculations in the NVE ensemble. Having implemented a 4th order symplectic integrator ...
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144 views

Number of microstates of discretized paths

Let us consider a square grid, which has been rotated by 45deg. On this grid we define a path, the directed polymer, which starts at the origin ($t = 0$) and extends in the positive $t$-direction ...
2
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1answer
1k views

Deriving the Sommerfeld expansion by contour integration (Le Bellac p. 277)

In Le Bellac's statistical physics book he derives the Sommerfeld expansion by a contour integral. The idea is to expand integrals of the type $I(\beta)\equiv \int_{0}^{\infty}d\epsilon\, ...
0
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2answers
427 views

How to compute configurations (entropy) of a system?

If we have a system $X$ consisting of subsystems $X_1$ and $X_2$. We also know that $X_1$ and $X_2$ have eigenstates $H_1 = 1 \times 10^{20}$ and $H_2 = 1 \times 10 ^{22}$. Can we calculate the ...
5
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0answers
105 views

Exact Beta Functions in Statistical Mechanics

I'm looking for analytically solvable models in statistical mechanics (classical or quantum) or related areas such as solid state physics in which the beta function for a certain renormalization ...
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1answer
371 views

relation between first law of thermodynamics and statistical mechanics definition of entropy

From the definition of entropy as $S= - Tr (\rho\, ln \rho)$ one obtains that $S = \frac{\langle E \rangle}{T} + \log Z.$ The first law of thermodynamics has $dS = {dE \over T}$. Why is there no ...
5
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2answers
465 views

Any example of lower symmetry in high temperature phase than the low temperature phase?

All the phase transition cases I came across so far have this property: the lower temperature phase has lower symmetry than the higher temperature one. But it is nowhere explicitly said that, lower ...
2
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1answer
85 views

What is the physical meaning of this simplification to calculate the effective coupling constants for a Gaussian model with quartic interactions?

To calculate the effective coupling constants $u'_2(q)$ and $u'_4(q)$ of the effective Hamiltinian eq (4.9) of this paper $$ H' = -\frac{1}{2}\int\limits_q u'_2(q)\sigma'_q\sigma'_{-q} - ...
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0answers
110 views

Statistical Mechanic

One can define entropy as $$S=k\log{\omega(E)},$$ where $\omega(E)$ is the numbers of states with energy equal $E$; and the canonical partition function for a set of N particles is defined ...
4
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3answers
435 views

Partition function of a gas of $N$ identical classical particles

Partition function of a gas of $N$ identical classical particles is given by $$ Z~=~\frac {1}{N! h^{3N}} \int \exp[-\beta H(p_1.......p_n, x_1....x_n)]d^3p_1...d^3p_n,d^3x_1...d^3x_n $$ in this ...
2
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0answers
172 views

Semiflexible discrete polymer chain

Suppose we have a 2D polymer model described by a set of 2D vectors {$\mathbf{t}_i$} ($i=1,2,\dots N$) of length $a$. The energy of the polymer is given by: $$ ...
10
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1answer
728 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 ...
0
votes
1answer
105 views

Indicators on how even the heat is distributed?

I'm wondering if there are any good indicators on how even the heat is distributed on an object (for simplicity, a flat object maybe)? What are the possibly reasonable ways to maximize the evenness if ...
4
votes
4answers
10k views

For an isolated system, can the entropy decrease or increase?

In any sizable system, the number of equilibrium states are much, much greater then the number of non-equilibrium states. Since each accessible micro state is equally probably, it is overwhelmingly ...
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2answers
2k views

Why should the Fermi level of a n-doped semiconductor be below the one of a p-doped?

In a pn-junction, the difference in Fermi level between the p doped and the n doped regions causes the apparition of a built-in electric field at equilibrium. This electric field goes from the n to ...
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2answers
2k views

Constant pressure and temperature mixing of 2 different ideal gases - possible work and heat?

A simple question I hope... Initially, have two separate containers of 2 different ideal gases, 1.) N1, P, T, V1 and 2.) N2, P, T, V2. After mixing, the pressure and temperature are still P and T, ...
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3answers
3k views

Partition function for quantum harmonic oscillator

Hi guys I'm currently trying to solve a mock exam for an exam in a few days and am a bit confused by the solutions they gave us for this exercise: Exercise: A solid is composed of N atoms which ...
3
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1answer
235 views

Nonpertubative renormalization in quantum field theory versus statistical physics

I am trying to work my head around how renormalization works for quantum field theory. Most treatments cover perturbative renormalization theory and I am fine with this approach. But it is not the ...
4
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3answers
635 views

What are the differences between indistinguishable and identical?

What is the difference between indistinguishable particles and identical particles?
7
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1answer
952 views

Postulate of a-priori probabilities

In Statistical Mechanics, we often postulate that for an isolated system, the phase-space density of all accessible microstates (i.e all microstates consistent with the energy) is the same. This is ...
2
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0answers
88 views

Stat mech explanation for separation of one liquid from another in gravity?

If one mixes two distinct ideal gases above the Earth's surface, one with a higher molecular mass than the other, then at equilibrium, their number density gradients will be such that at low heights, ...
6
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1answer
960 views

Maximum Principle vs. Minimum Principle in Non-equilibrium Thermodynamics

Prigogine's Min. principle states that in steady-state non-equilibrium systems the entropy generation rate is at a minimum, i.e., a system will seek a steady-state that has min entropy generation. ...
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2answers
1k views

Does chaos theory occur in quantum mechanics? Or in any non-newtonian physics?

Does chaos theory occur in quantum mechanics? Or in any non-newtonian physics? Apart from perhaps thermodynamics?
37
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4answers
2k 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 ...
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2answers
1k 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 ...
5
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1answer
232 views

Are isolated many-particle quantum systems always in a pure state?

I am trying to understand pure and mixed states better. If I have N quantum particles in an isolated system. The many-particle state is a superposition of the product of single-particle states by the ...
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0answers
48 views

Any new texts directly on second law of thermodynamics? [duplicate]

Possible Duplicate: Recommendations for Statistical Mechanics book Is anyone aware of any recent text that summarises the research and arguments on second law of thermodynamics and also on ...
2
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2answers
371 views

Examples of systems with energy as an intensive variable

I need to consider a couple of examples of systems which have energies that are intensive variables - not extensive. I'be been thinking about this and I am not coming up with anything. My ...
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2answers
3k views

Calculate temperature of the earth through blackbody radiation

I don't understand the solutions to a problem about blackbody radiation and was wondering if anybody could help me out. Here is the question: The sun can be considered as a blackbody radiation ...
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2answers
139 views

Where and how is the entropy of a black hole stored?

Where and how is the entropy of a black hole stored? Is it around the horizon? Most of the entanglement entropy across the event horizon lies within Planck distances of it and are short lived. Is ...
15
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3answers
552 views

Could temperature have been defined as $-\partial S/\partial U$?

When coming up with a definition of temperature, it's typical to start with an empirical definition that a system with a hotter temperature tends to lose heat to a system with a colder temperature. ...
2
votes
3answers
640 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 ...
4
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0answers
144 views

Thermal equilibrium and non correlations

I read in a book on quantum fluctuations and quantum noise that, at thermal equilibrium the classical canonical variables are uncorrelated, ie: $$\langle xp\rangle=\langle x\rangle\langle p\rangle$$ ...
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1answer
303 views

Reasons for violation of universality in statistical mechanics

The Universality in statistical mechanics is nicely explained by the renormalization group theory. However, there are fair amount of numerical and theoretical studies show that it can be violated in ...
4
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1answer
1k views

Helmholtz Free Energy, Partition Function

I'm trying to develop some basic intuition here, so this comes mostly as a jumble of commentary/questions. Hope its acceptable. Helmholtz Free Energy: $A = -{\beta ^{-1}}lnZ$. I find this statement ...
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1answer
127 views

Parameter determining argon phase

Currently I am working a molecular simulation to determine phases of an argon NPT ensemble using Lennard Jones potential. Mainly I use the radial distribution function to determine solid, liquid, or ...
2
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2answers
243 views

Computing microstate probabilities based on Boltzmann distribution for chemical systems - Is it rigorous?

One approach to predicting the folded structure of a polymer (DNA, RNA, protein) is to compute the probability that any particular part of the polymer $x_i$ is "paired" with another part of the ...
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0answers
191 views

helmholtz free energy of a polymer

You have a polymer chain of $N$ units, which is represented by $N$ independent springs in series. The springs are Hookean, with spring constant $L$, and the end to end vector is $\mathbf r$. So the ...
2
votes
2answers
311 views

Phase volume contraction in dissipative systems

I am confused about phase-volume contraction in dissipative systems. Please help me catch the flaw in my understanding. From a macroscopic point of view I understand that a dynamic system tends to go ...
2
votes
3answers
2k views

Fermi's Golden Rule and Density of States

I know Fermi's Golden Rule in the form $$\Gamma_{fi} ~=~ \sum_{f}\frac{2\pi}{\hbar}\delta (E_f - E_i)|M_{fi}|^2$$ where $\Gamma_{fi}$ is the probability transition rate, $M_{fi}$ are the transition ...
3
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1answer
113 views

Freedom in the Choice of a Beta Functions in RG

Assume we're given a certain statistical model, say the infinite range Ising model \begin{equation} H_{N}\{\vec\sigma_{N}\}~=~ - \frac{x_{N}}{2N} \sum_{i,j =1}^{N} \sigma_{i} \sigma_{j} ...
8
votes
3answers
257 views

Is $k_B \rightarrow 0$ the classical limit of stat. mech., as $\hbar \rightarrow 0$ is in QM?

I hear very often among my peers and seniors that just as how $\hbar\rightarrow0$ takes me to classical mechanics from quantum mechanics, $k_B\rightarrow0$ will take me to classical thermodynamics ...
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1answer
372 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. ...
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1answer
271 views

Why does Physica A journal contain economics papers? [closed]

Why does Physica A journal contain economics papers? Like this: Steve Keen, Russell Standish. Profit maximization, industry structure, and competition: A critique of neoclassical theory. Physica A ...
6
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1answer
354 views

few fermions in a harmonic trap — position density matrix from diagrammatics

I'm trying to calculate the momentum distribution of a 1D system of non-interacting identical fermions in a harmonic trap. Given Feynman's answer (from his Statistical Mechanics book) for the ...
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0answers
74 views

Why is the transition into N proportional to N+1?

I am having trouble understanding the origin of the bosonic stimulated emission. How can I qualitatively understand why bosons Boson's attract each other into similar quantum states. The furtherst I ...