The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.
12
votes
3answers
881 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 ...
6
votes
5answers
999 views
Recommendations for Statistical Mechanics book
I saw Book recommendations
No reference to Statistical Mechanics there.
I learned thermodynamics and the basics of statistical mechanics but I'd like to
sit through a good advanced book/books.
Mainly ...
4
votes
4answers
346 views
Chance of objects going against greater entropy
My book uses the argument that the multiplicities of a few macrostates in a macroscopic object take up an extraordinarily large share of all possible microstates, such that even over the entire ...
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 ...
6
votes
3answers
947 views
Maxwell's Demon Constant (Information-Energy equivalence)
New Scientist article: Summon a 'demon' to turn information into energy
The speed of light c converts between space and time and also appears in e=mc^2.
Maxwell's Demon can turn information supplied ...
2
votes
1answer
274 views
Cross-field diffusion from Smoluchowski approximation
I'm reading An Introduction to Stochastic Processes in Physics by Don S Lemons. Problem 10.2 leads to a pair of equations:
$dV_x = -\gamma V_xdt+V_y\Omega dt-V_y\sqrt{2\gamma dt}N_t(0,1)$
$dV_y = ...
6
votes
6answers
650 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 ...
5
votes
3answers
386 views
Are negative temperatures typically associated with negative absolute pressures?
Negative temperatures and negative absolute pressures are both possible in physical systems. Negative temperatures arise in (for example) populations of two-state systems, which have a maximum amount ...
5
votes
5answers
2k views
Why was the universe in a extraordinarily low-entropy state right after the big bang?
Let me start by saying that I have no scientific background whatsoever. I am very interested in science though and I'm currently enjoying Brian Greene's The Fabric of the Cosmos. I'm at chapter 7 and ...
11
votes
3answers
1k 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 ...
4
votes
4answers
497 views
Are the physical laws scale-dependent?
If you read the article "More Is Different", by P.W. Anderson (Science, 4 August 1972), you will find a deep question: are the physical laws dependent of the size of the system under study?
As an ...
15
votes
7answers
622 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 ...
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.
...
10
votes
2answers
979 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 ...
5
votes
4answers
2k views
Chemical potential
This is something probably very basic but I was led back to this issue while listening to a recent seminar by Allan Adams on holographic superconductors. He seemed very worried to have a theory at ...
7
votes
3answers
860 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 ...
6
votes
7answers
471 views
Is it wrong to talk about wave functions of macroscopic bodies?
Does a real macroscopic body, like table, human or a cup permits description as a wave function? When is it possible and when not?
For example in the "Statistical Physics, Part I" by Landau & ...
6
votes
1answer
445 views
The equipartition theorem in momentum space
Motivated by the answers to this question on turbulence, I'm interested in an explanation and/or derivation/reference of the equipartition theorem in momentum space. To formulate it as a question:
...
5
votes
4answers
497 views
Please clarify how entropy increases when matter gravitationally coalesces
On John Baez's website, http://math.ucr.edu/home/baez/entropy.html, he discusses the problem of how entropy increases when a cloud of ideal gas collapses gravitationally (no black holes - keeping it ...
2
votes
1answer
116 views
Clear up confusion about the meaning of entropy
So I though, and was told, that entropy is the amount of disorder in a system. Specifically the example of heat flow and it flows to maximize entropy. To me this seemed odd. This seemed more ordered ...
20
votes
4answers
773 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 ...
8
votes
3answers
271 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. ...
7
votes
2answers
343 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?
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 ...
5
votes
1answer
271 views
Motivation for maximum Renyi/Tsallis entropy
The Conditional limit theorem of Van Campenhout and Cover gives a physical reason for maximizing (Shannon) entropy.
Nowadays, in statistical mechanics, people talk about maximum Renyi/Tsallis entropy ...
10
votes
4answers
606 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 $\rho_0=\frac{1}{Z}e^{-\beta H}$ ...
9
votes
1answer
604 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 ...
4
votes
2answers
253 views
How and why can random matrices answer physical problems?
Random matrix theory pops up regularly in the context of dynamical systems.
I was, however, so far not able to grasp the basic idea of this formalism. Could someone please provide an instructive ...
4
votes
1answer
379 views
Hit a bottle of beer on the top with another causes the first to spit all the gas, why?
So, on the other day me and my colleges were discussing the following phenomena:
Pick two open bottles of beer. With the bottom of the first, hit the second on the bottleneck, in the following way: ...
5
votes
0answers
259 views
Is the “particle number” of “electrons” well defined in Wen's string-net theory of elementary particles?
According to professor Wen's string-net theory(Colloquium: Photons and electrons as emergent phenomena, Levin and Wen, Rev. Mod. Phys. 77, 871(2005), see e.g. http://arxiv.org/abs/cond-mat/0407140), ...
4
votes
3answers
324 views
Is there a mechanism for time symmetry breaking?
Excluding Thermodynamic's arrow of time, all mathematical descriptions of time are symmetric. We know the arrow of time is real and we know the equations describing physics are real so is there any ...
4
votes
3answers
246 views
How many particles is needed to observe a phase transition?
This is a question that was rised when we were discussing "what is melting actually". How many particles you need to form a liquid or solid. I have some remarks to point out what I want to know.
Q: ...
4
votes
2answers
2k views
How to derive Fermi-Dirac and Bose-Einstein distribution using canonical ensemble?
My textbook says that microcanonical ensemble, canonical ensemble and grand canonical ensemble are essentially equivalent under thermodynamic limit. It also derives Fermi-Dirac and Bose-Einstein ...
3
votes
1answer
176 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 ...
1
vote
1answer
592 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 ...
15
votes
4answers
173 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 ...
9
votes
3answers
822 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 ...
8
votes
5answers
395 views
Why does the Boltzmann factor $e^{-E/kT}$ seem to imply that lower energies are more likely?
I'm looking for an intuitive understanding of the factor $$e^{-E/kT}$$ so often discussed. If we interpret this as a kind of probability distribution of phase space, so that $$\rho(E) = ...
6
votes
1answer
163 views
Thermodynamic limit “vs” the method of steepest descent
Let me use this lecture note as the reference.
I would like to know how in the above the expression (14) was obtained from expression (12).
In some sense it makes intuitive sense but I would ...
6
votes
1answer
262 views
What is the information geometry of 1D Ising model for a complex magnetic field?
Consider the one-dimensional Ising model with constant magnetic field and node-dependent interaction on a finite lattice, given by
$$H(\sigma) = -\sum_{i = 1}^N J_i\sigma_i\sigma_{i + 1} - h\sum_{i = ...
4
votes
3answers
489 views
What are some of the best books on complex systems?
I'm rather interested in getting my feet wet at the interface of complex systems and emergence. Can anybody give me references to some good books on these topics? I'm looking for very introductory ...
3
votes
3answers
257 views
Does entropy really always increase (or stay the same)? [duplicate]
Consider this image. If the big (grey) molecules were all to spontaneously move to the left, and the small ones were to move to the right, there would be an increase in order.
While unlikely, ...
2
votes
1answer
232 views
What is non-thermal plasma?
I read about non-thermal plasma, but I still have some questions:
The ions and neutral particles are not in thermal equilibrium with the electron, does that mean that the overall temperature is low ...
1
vote
4answers
337 views
Irreversible expansion and time reversal symmetry
Suppose there are N non-interacting classical particles in a box, so their state can be described by the $\{\mathbf{x}_i(t), \mathbf{p}_i(t) \}$. If the particles are initially at the left of the box, ...
0
votes
2answers
216 views
Reconstruction of information stored in an evaporating black hole from the emission spectrum?
For simple setups, where the radiation field deviates not too far from thermodynamic equilibrium (< 10 %), corrections to the Planckian thermal emission spectrum can be calculated (and measured) ...
6
votes
2answers
233 views
Mathematical probabilistic interepretation of probability amplitude
As a warning, I come from an "applied math" background with next to no knowledge of physics. That said, here's my question:
I'm looking at the possibility of using probability amplitude functions to ...
5
votes
2answers
333 views
The analogy between temperature and imaginary time
There are many statements about the relation between time and temperature in statistical physics and quantum field theory, the basic idea is to interpret (inverse) temperature in statistics as "time" ...
5
votes
1answer
380 views
What does the concept of phase space mean in particle physics?
I came across the concept of phase space in statistical mechanics.
How does this concept come about in particle physics?
Why was it introduced and how is it used?
What does it mean when ...
4
votes
4answers
218 views
Why can $\beta$ not be linearly proportional to $T$, that is $\beta = constant \times T$?
$\beta$ in statistical mechanics is equal to $\frac{1}{k_BT}$ in in thermodynamics, but I do not understand why $\beta\propto T^{-1}$ instead of, say, $\beta\propto T$?
3
votes
0answers
80 views
Spontaneous conversion of heat into work at negative temperatures
Consider a heavy macroscopic object moving in a gas. Friction causes its kinetic energy to be converted into heat. Thermodynamically, there is (effectively) no entropy associated with the kinetic ...
