The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.
51
votes
6answers
844 views
What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis?
This question was listed as one of the questions in the proposal (see here), and I didn't know the answer. I don't know the ethics on blatantly stealing such a question, so if it should be deleted or ...
28
votes
1answer
158 views
$(\mu,P,T)$ pseudo-ensemble: why is it not a proper thermodynamic ensemble?
While teaching statistical mechanics, and describing the common thermodynamic ensembles (microcanonical, canonical, grand canonical), I usually give a line on why there can be no $(\mu, P, T)$ ...
23
votes
5answers
288 views
What are some critiques of Jaynes' approach to statistical mechanics?
Suggested here: What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis?
I was wondering about good critiques of Jaynes' approach to statistical ...
22
votes
1answer
175 views
Mermin-Wagner theorem in the presence of hard-core interactions
It seems quite common in the theoretical physics literature to see applications of the "Mermin-Wagner theorem" (see wikipedia or scholarpedia for some limited background) to systems with hard-core ...
20
votes
5answers
77 views
Connections and applications of SLE in physics
In probability theory, the Schramm–Loewner evolution, also known as stochastic Loewner evolution or SLE, is a conformally invariant stochastic process. It is a family of random planar curves that are ...
20
votes
4answers
743 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 ...
19
votes
3answers
126 views
Does entropy measure extractable work?
Entropy has two definitions, which come from two different branches of science: thermodynamics and information theory. Yet, they both are thought to agree. Is it true?
Entropy, as seen from ...
15
votes
7answers
598 views
How is $\frac{dQ}{T}$ measure of randomness of system?
I am studying entropy and its hard for me to catch up what exactly is entropy.
Many articles and books write that entropy is the measure of randomness or disorder of the system. They say when a gas ...
15
votes
4answers
165 views
What is a simple intuitive way to see the relation between imaginary time (periodic) and temperature relation?
I guess I never had a proper physical intuition on, for example, the "KMS condition". I have an undergraduate student who studies calculation of Hawking temperature using the Euclidean path integral ...
15
votes
0answers
105 views
Systematic approach to deriving equations of collective field theory to any order
The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
14
votes
2answers
820 views
Is this Landau's other critical phenomena mistake?
There was an old argument by Landau that while the liquid gas transition can have a critical point, the solid-liquid transition cannot. This argument says that the solid breaks translational symmetry, ...
13
votes
4answers
2k views
What does Peter Parkers formula represent?
Okay, so the trailer for the new Spider Man movie is out and appearently our friendly physicist from the neightborhood came up with something. However I can't find out what this is.
...
13
votes
3answers
1k views
Home experiment to estimate Avogadro's number?
How to get an approximation of Avogadro or Boltzmann constant through experimental means accessible by an hobbyist ?
13
votes
1answer
349 views
Onsager's Regression Hypothesis, Explained and Demonstrated
Onsager's 1931 regression hypothesis asserts that “…the average regression of fluctuations will obey the same laws as the corresponding macroscopic irreversible process". (Here is the links to ...
13
votes
1answer
72 views
Phase Transition in the Ising Model with Non-Uniform Magnetic Field
Consider the Ferromagnetic Ising Model ($J>0$) on the lattice $\mathbb{Z}^2$ with the Hamiltonian with boundary condition $\omega\in\{-1,1\}$ formally given by
$$
...
13
votes
2answers
29 views
Sampling typical clusters between distant points in subcritical percolation
I have on several occasions wondered how one might proceed in order to sample large subcritical Bernoulli bond-percolation clusters, say on the square lattice.
More precisely, let's consider the ...
12
votes
3answers
1k views
How do you prove $S=-\sum p\ln p$?
How does one prove the formula for entropy $S=-\sum p\ln p$?
Obviously systems on the microscopic level are fully determined by the microscopic equations of motion. So if you want to introduce a law ...
11
votes
3answers
859 views
Prove that negative absolute temperatures are actually hotter than positive absolute temperatures
Could someone provide me with a mathematical proof of why, a system with an absolute negative Kelvin temperature (such that of a spin system) is hotter than any system with a positive temperature (in ...
11
votes
3answers
972 views
How Non-abelian anyons arise in solid-state systems?
Recently it has been studied non-abelian anyons in some solid-state systems. These states are being studied for the creation and manipulation of qubits in quantum computing.
But, how these ...
11
votes
2answers
70 views
Discussions of the axioms of AQFT
The most recent discussion of what axioms one might drop from the Wightman axioms to allow the construction of realistic models that I'm aware of is Streater, Rep. Prog. Phys. 1975 38 771-846, ...
10
votes
4answers
584 views
Ignorance in statistical mechanics
Consider this penny on my desc. It is a particular piece of metal,
well described by statistical mechanics, which assigns to it a state,
namely the density matrix $\rho_0=\frac{1}{Z}e^{-\beta H}$ ...
10
votes
2answers
348 views
Can $10^{23}$ stars be treated with methods of statistical mechanics?
Statistical mechanics is used to describe systems with large number of particles ~$10^{23}$.
The observable universe contains between $10^{22}$ to $10^{24}$ stars. Can we treat those many stars as a ...
10
votes
1answer
341 views
Why is the partition function called ''partition function''?
The partition function plays a central role in statistical mechanics.
But why is it called ''partition function''?
10
votes
2answers
289 views
What is known about some massive Gaussian models on a lattice?
Recently I started to play with some massive Gaussian models on a lattice. Motivation being that I work on massless models and want to understand the massive case because it seems easier to handle ...
9
votes
6answers
679 views
A die versus a quantum experiment
Let suppose you roll a die, and it falls into a hidden place, for example under furniture.
Then although the experiment has already been made (the die already has a number to show), that value can not ...
9
votes
4answers
2k views
Difference between thermodynamics and statistical mechanics
I've just finished a class a few weeks ago which taught thermo and stat mech, and I still don't know the exact difference between the two. Can someone help clear this up for me? (Yeah it's sad, and ...
9
votes
2answers
934 views
Ising model for dummies
I am looking for some literature on the Ising model, but I'm having a hard time doing so. All the documentation I seem to find is way over my knowledge.
Can you direct me to some documentation on it ...
9
votes
4answers
782 views
How many Onsager's solutions are there?
Update: I provided an answer of my own (reflecting the things I discovered since I asked the question). But there is still lot to be added. I'd love to hear about other people's opinions on the ...
9
votes
3answers
221 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 ...
9
votes
2answers
917 views
trying to understand Bose-Einstein Condensate (BEC)
I am a computer scientist interested in network theory. I have come across the Bose-Einstein Condensate (BEC) because of its connections to complex networks. What I know about condensation is the ...
9
votes
1answer
39 views
Renyi fractal dimension $D_q$ for non-trivial $q$
For a probability distribution $P$, Renyi fractal dimension is defined as
$$D_q = \lim_{\epsilon\rightarrow 0} \frac{R_q(P_\epsilon)}{\log(1/\epsilon)},$$
where $R_q$ is Renyi entropy of order $q$ ...
9
votes
1answer
360 views
What are some predictions from string theory that say some crystalline materials “will end up in one of many lowest-energy ground states?”
I am referring to this recent "news feature" by Zeeya Merali from Nature magazine www.nature.com/uidfinder/10.1038/478302a. Here is the specific quote:
"To make matters worse, some of the testable ...
9
votes
1answer
578 views
Largest theoretically possible specific heat capacity?
What substance will have the largest specific heat capacity integrated from T=0 to, say, room temperature? In other words, given a finite amount of mass, what object or collection of objects has the ...
9
votes
1answer
152 views
Reduced density matrices for free fermions are thermal
Many recent papers study entanglement in eigenstates of fermionic free hamiltonians (normally on a lattice) using the basic assumption that the reduced density matrices are thermal (e.g. Peschel ...
9
votes
3answers
319 views
Can the entropy density of a spacelike singularity arbitrarily exceed the inverse Planck volume?
For the purpose of this question, let's restrict ourselves to BKL singularities. BKL cosmologies are homogeneous Bianchi type XIII and IV cosmologies which exhibit oscillatory chaotic behavior, ...
9
votes
3answers
806 views
To calculate the correlation functions of an XX spin chain, Wick's theorem is used. But is it valid for a chain of any size?
The correlation functions found in Barouch and McCoy's paper (PRA 3, 2137 (1971)) for the XX spin chain use a method which uses Wick's theorem. For the zz correlation function, this gives
$\langle ...
9
votes
2answers
474 views
Transforming a sum into an integral
I posted this in the mathematical forums. Maybe you will help me. I found an hard article http://prola.aps.org/abstract/PR/v105/i3/p776_1 of yang huang and luttinger. The authors begins with the sum: ...
9
votes
0answers
52 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 ...
8
votes
7answers
795 views
Is there a four-dimensional definition of entropy?
It seems odd that entropy is usually only defined for a system in a single 'slice' of time or spacelike region. Can one define the entropy of a system defined by a 4d region of spacetime, in such a ...
8
votes
2answers
360 views
Shaking a jar of balls
A jar is filled with two types of balls, red and green. Red balls have radius $r_1$ and mass $m_1$, green balls have radius $r_2$ and mass $m_2$.
If initially the balls are randomly placed throughout ...
8
votes
1answer
101 views
Do thermodynamic quantities in CFT correspond to something different in AdS/CFT?
From what I've (hopefully) understood from the AdS/CFT correspondence, physical quantities have a dual version. For example, the position in the bulk is the scale size (in renormalization), and waves ...
8
votes
3answers
260 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. ...
8
votes
3answers
178 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 ...
8
votes
1answer
99 views
Why are topological solitons present in some phases for lattice models?
Over a spatial continuum, it is easy to see why some topological solitons like vortices and monopoles have to be stable. For similar reasons, Skyrmions also have to be stable, with a conserved ...
8
votes
0answers
145 views
How is the logarithmic correction to the entropy of a non extremal black hole derived?
I`ve just read, that for non extremal black holes, there exists a logarithmic (and other) correction(s) to the well known term proportional to the area of the horizon such that
$S = \frac{A}{4G} + K ...
8
votes
3answers
202 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 ...
7
votes
5answers
1k views
Can a single classical particle have any entropy?
recently I have had some exchanges with @Marek regarding entropy of a single classical particle.
I always believed that to define entropy one must have some distribution. In Quantum theory, a single ...
7
votes
2answers
365 views
Why doesn't the percentage of oxygen in Earth's atmosphere diminish significantly with altitude?
According to numerous sources online, the percentage of oxygen is approximately the same at sea level and 10,000 meters. Since oxygen is heavier than nitrogen, shouldn't the percentage of oxygen ...
7
votes
2answers
284 views
What does the chromatic polynomial have to do with the Potts model?
Wikipedia writes:
In statistical mechanics, the Potts
model, a generalization of the Ising
model, is a model of interacting spins
on a crystalline lattice.
From combinatorics conferences ...
7
votes
3answers
851 views
Once a quantum partition function is in path integral form, does it contain any operators?
Once a quantum partition function is in path integral form, does it contain any operators?
I.e. The quantum partition function is $Z=tr(e^{-\beta H})$ where H is an operator, the Hamiltonian of the ...
