A important property of all systems in thermodynamics and statistical mechanics. Entropy characterizes the degree to which the energy of the system is *not* available to do useful work
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945 views
What is information?
We're all familiar with basic tenants such as "information cannot be transmitted faster than light" and ideas such as information conservation in scenarios like Hawking radiation (and in general, ...
20
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3answers
238 views
An entropy of the Wigner function
Is there an entropy that one can use for the Wigner quasi-probability distribution?
(In the sense of a phase-space probability distribution, not - just von Neumann entropy.)
One cannot simply use ...
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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 ...
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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 ...
13
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4answers
854 views
Entropy of radiation emitted into space
In several papers I see something equivalent to the following expression for the entropy of radiation given by an astronomical object such as the Sun (assuming the object can be approximated as a ...
12
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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 ...
12
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6answers
658 views
How can it be that the beginning universe had a high temperature and a low entropy at the same time?
The Big Bang theory assumes that our universe started from a very/infinitely dense and extremely/infinitely hot state. But on the other side, it is often claimed that our universe must have been ...
11
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5answers
670 views
Why does the nature always prefer low energy and maximum entropy?
Why does the nature always prefer low energy and maximum entropy?
I've just learned electrostatics and I still have no idea why like charges repel each other.
...
11
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2answers
334 views
The entropic cost of tying knots in polymers
Imagine I take a polymer like polyethylene, of length $L$ with some number of Kuhn lengths $N$, and I tie into into a trefoil knot. What is the difference in entropy between this knotted polymer and ...
10
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4answers
585 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
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3answers
1k views
Is there any proof for the 2nd law of thermodynamics?
Are there any analytical proofs for the 2nd law of thermodynamics?
Or is it based entirely on empirical evidence?
9
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2answers
224 views
black hole no-hair theorems vs. entropy and surface area
I was revisiting some old popular science books a while ago and two statements struck me as incompatible.
No-hair theorems: a black hole is fully-described by just a few numbers (mass, spin etc) ...
9
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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 $q$ ...
8
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3answers
750 views
How efficient is a desktop computer?
As I understand it (and admittedly it's a weak grasp), a computer processes information irreversibly (AND gates, for example), and therefore has some minimum entropy increase associated with its ...
8
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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
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4answers
411 views
Did really everything begin with a state with very low entropy?
As emphasized by Penrose many years ago, cosmology can only make sense if the world
started in a state of exceptionally low entropy. The low entropy starting point is the
ultimate reason that the ...
8
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3answers
1k views
Why does the low entropy at the big bang require an explanation? (cosmological arrow of time)
I have read Sean Carrol's book. I have listened to Roger Penrose talk on "Before the Big Bang". Both are offering to explain the mystery of low entropy, highly ordered state, at the Big Bang.
Since ...
8
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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
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3answers
203 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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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
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1answer
202 views
Area law for Entropy in Loop Quantum Gravity
In connection with the long saga of the (claimed) microscopic
calculations of the Hawking-Bekenstein entropy in (3+1) Loop Quantum Gravity (LQG) and related approaches I have the following question: ...
6
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5answers
698 views
How is thermodynamic entropy defined? What is its relationship to information entropy?
I read that thermodynamic entropy is a measure of the number of microenergy states. What is the derivation for $S=k\log N$, where $k$ is Boltzmann constant, $N$ number of microenergy states.
How is ...
6
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4answers
351 views
Second Law of Thermodynamics and the Arrow of Time: Why isn't time considered fundamental?
I've come across this explanation that the "arrow of time" is a consequence of the second law of thermodynamics, which says that the entropy of an isolated system is always increasing. The argument is ...
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6answers
623 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 ...
6
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3answers
915 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 ...
6
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2answers
188 views
Renyi entropy in physical systems
We know that the Shannon entropy $H(P)=- k_{\mathrm{B}}\sum_i p_i \ln p_i$ is mostly the entropy of the thermodynamic systems.
Does the Renyi measure $H_{\alpha}(P)=\frac{1}{1-\alpha}\log \sum ...
6
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1answer
174 views
Does measurement, quantum in particular, always increase the total entropy?
Measurement of a quantum observable (in an appropriate, old-fashioned sense) necessarily involves coupling to a system with a macroscopically large number of degrees of freedom.
Entanglement with this ...
6
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1answer
184 views
Nonextensive statistical mechanics
I know that the Tsallis($S_q$) entropy is called nonextensive information measure in the sense that if $P$ and $Q$ are two probability distributions then $S_q(P\times ...
5
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3answers
295 views
Confusion regarding entropy, reference papers request
1.a In paragraph at Wikipedia/Entropy it is stated:
This is because energy supplied at a high temperature (i.e. with low entropy)
tends to be more useful than the same amount of energy
...
5
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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 ...
5
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3answers
4k views
Do magnets lose their magnetism?
I recently bought some buckyballs, considered to be the world's best selling desk toy. Essentially, they are little, spherical magnets that can form interesting shapes when a bunch of them are used ...
5
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3answers
2k views
Why does maximal entropy imply equilibrium?
From a purely thermodynamical point of view, why does that entropy have to be a maximum at equilibrium? Say there is equilibrium, i.e. no net heat flow, why can the entropy not be sitting at a ...
5
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1answer
264 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 ...
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2answers
184 views
Order = Energy = Mass?
Here is a following problem I encountered when chatting about physics with my friend:
Let us imagine a classical example of ordered state of matter in thermodynamic sense: let's take a cylinder ...
5
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3answers
546 views
Entropy and the principle of least action
Is there any link between the law of maximum entropy and the principle of least action. Is it possible to derive one from the other ?
5
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2answers
161 views
Information Loss in annihilation
The concept of information loss is usually discussed with respect to a black hole. My understanding is that whatever matter you put into the black hole, it has only 3 "hairs" and so one doesn't know, ...
5
votes
2answers
440 views
Experiments that measure the time a gas takes to reach equilibrium
If you take two ideal gases at different temperatures, and allow them to share energy through heat, they'll eventually reach a thermodynamic equilibrium state that has higher entropy than the ...
5
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1answer
67 views
What happens at the interface between two universes with opposite thermodynamic arrows of time?
I was trying to think but cannot figure it out. For instance, if the interaction is small, for instance limited to a windows, the observers in each universe will see that the other goes in reverse. ...
5
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2answers
928 views
Why do reversible processes not increase the entropy of the universe infinitesimally?
The book Commonly Asked Questions in Thermodynamics states:
When we refer to the passage of the system through a sequence of internal equilibrium states without the establishment of equilibrium ...
5
votes
1answer
219 views
Energy formula for separating $O_2$ from mixture of $O_2$, $NH_3$ and $H_2O$
I have a physics problem I'd like to make sure I get correct.
The practical aspect of this problem is that the photosynthetic efficiency of algae is inhibited with dissolved O2 in the growth medium, ...
5
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0answers
88 views
Geometric entropy vs entanglement entropy (dependent on curvature coupling parameter)
I have a quick question. In hep-th/9506066, Larsen and Wilczek calculated the geometric entropy (which I believe is just another name for entanglement entropy) for a non-minimally coupled scalar field ...
4
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2answers
463 views
Entropy of an empty universe
After watching the first episode of wonders of the solar system, one question came up which is not explained.
Bryan Cox says that ultimately the universe will be devoid of matter, so not even a ...
4
votes
3answers
319 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
410 views
Second law of thermodynamics and a bunch of magnets
Say I put a bunch of powerful square magnets on a nearly frictionless table in a disordered fashion. The second law of thermodynamics states that the system shall spontaneously get more disordered, ...
4
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3answers
163 views
Definition of entropy
In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) entropy of a variable $X$ is ...
4
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3answers
233 views
Is a world with constant/decreasing entropy theoretically impossible?
I'm not 110% sure exactly what I mean by this question. It was sparked by a friend who said he wished the law of entropy were reversed, so he wouldn't have to worry about cleaning the bathroom.
...
4
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3answers
644 views
How to understand temperatures of different degrees of freedom?
So I'm reading this book, where after the preface and before the models there is a section called General Notions and Essential Quantities, which introduce some things I don't understand. They regard ...
4
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2answers
70 views
What is the entropy of a system when its volume tends to zero?
Say that a closed system has $n$ dimensions and is in the shape of a $n$-ball with a radius of 1, it's volume will be
$$\frac{\pi^\frac{n}{2}}{\Gamma(\frac{n}{2}+1)}$$
which tends to 0 yet is not ...
4
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1answer
85 views
name of experiment
I'm seeking the name of or reference for an experiment I once saw in a college physics class. At the beginning of one class the instructor repeatedly wound a wiper that spread a blot of some type of ...
4
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2answers
216 views
What's the validity of the thermodynamic definition of entropy?
Thermodynamic Entropy Variation is defined as
$$\Delta S = \int_i^f \frac{dQ}{T},$$
where $i$ and $f$ are the initial and final states of the process.
My question is: does this equation apply to ...
