The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.
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3answers
137 views
Why do we need different ensembles in statistical mechanics?
Why do we study these different ensembles, microcanonical, canonical, grand canonical ensemble ? Are they used for studying different physical system or scenarios?(e.g. in some system you can only ...
2
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1answer
63 views
How can dQ/T be interpreted as a system's level of disorder?
Long before statistical mechanics, entropy was introduced as:
$dS = \frac{dQ}{T}$
At the time when entropy was introduced in this manner, was it known that entropy represents how "disordered" a ...
2
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0answers
82 views
Why is the free energy minimized by the Boltzmann distribution?
Can someone show me, without glossing over anything, why $F = E - TS$ is minimized when $p_i = e^{-U_i/k_bT}/\sum_ie^{-U_i/k_bT}$? I understand it conceptually, but am having difficulty showing it ...
2
votes
0answers
53 views
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 ...
0
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0answers
42 views
Gas of hard-core spheres
Consider a system of hard spheres of diameter $d_0$ at temperature $T$ and $V/N=v$. Discuss briefly the existence of the thermodynamic limit for the Helmholtz free energy on the basis of the ...
2
votes
1answer
154 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
votes
1answer
154 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 $\mathbf{d|\vec{q_{i}}|}$; ...
8
votes
3answers
205 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 ...
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2answers
213 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 ...
0
votes
0answers
71 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
votes
1answer
248 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\, ...
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2answers
142 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 ...
4
votes
0answers
69 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 ...
0
votes
1answer
118 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 ...
2
votes
2answers
91 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
votes
1answer
67 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
$$ H' = -\frac{1}{2}\int\limits_q u'_2(q)\sigma'_q\sigma'_{-q}
- ...
1
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0answers
75 views
Statistical Mechanic
One can define entropy as $$S=k\log{\omega(E)},$$ where $\omega(E)$ is the numbers of states with energy equal $E$; and the canonical partition function for a set of N particles is defined ...
4
votes
3answers
164 views
Partition function of a gas of $N$ identical classical particles
Partition function of a gas of $N$ identical classical particles is given by
$$ 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 $$
in this ...
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votes
0answers
18 views
Rice Allnatt distribution function
Can anyone give me an article of which explains Rice Allnatt distribution function or can you explain the function here?
2
votes
0answers
47 views
Semiflexible discrete polymer chain
Suppose we have a 2D polymer model described by a set of 2D vectors {$\mathbf{t}_i$} ($i=1,2,\dots N$) of length $a$.
The energy of the polymer is given by:
$$
...
3
votes
1answer
160 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
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1answer
59 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 ...
3
votes
5answers
663 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 ...
1
vote
2answers
223 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 ...
1
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1answer
224 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, ...
1
vote
3answers
480 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 ...
2
votes
0answers
100 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 ...
2
votes
2answers
162 views
What are the differences between indistinguishable and identical?
What is the difference between indistinguishable particles and identical particles?
5
votes
1answer
84 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
votes
0answers
76 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
votes
1answer
246 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. ...
7
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2answers
311 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?
20
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4answers
748 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 ...
3
votes
2answers
278 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
votes
1answer
127 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 ...
1
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0answers
38 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
votes
2answers
141 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 ...
1
vote
1answer
297 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 ...
4
votes
1answer
88 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 ...
8
votes
3answers
262 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. ...
0
votes
2answers
194 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
votes
0answers
112 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: $$\langle xp\rangle=\langle x\rangle\langle p\rangle$$
...
4
votes
1answer
202 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 ...
2
votes
1answer
383 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 ...
1
vote
1answer
84 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
votes
2answers
124 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 ...
1
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0answers
90 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 ...
0
votes
0answers
50 views
energy and number of configurations for particular microstate [closed]
there are N molecules on an interface of A sites. if the molecule is perpendicular to the interface, it has an energy of -b, and if it is parallel to the interface it has an energy of -d (b>d>0). Let ...
1
vote
1answer
140 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 ...
2
votes
1answer
132 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 ...
