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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Is it necessary to consume energy to perform computation?

As far as I know, today most of the computers are made from semiconductor devices, so the energy consumed all turns into the heat emitted into space. But I wonder, is it necessary to consume energy ...
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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, ...
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Why is information indestructable?

I really can't understand what Leonard Susskind means when he says that information is indestructible. Is that information that is lost, through the increase of entropy really recoverable? He ...
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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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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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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 ...
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Intuitive understanding of the entropy equation

In thermodynamics, entropy is defined as $ d S = \dfrac{\delta q_{\rm }}{T}$. This definition guarantees that heat will transfer from hot to cold, which is the second law of thermodynamics. But, why ...
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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 ...
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Why isn't absolute $0 K$ temperature possible?

So $T$ is defined as $$T = \left(\frac{\partial E}{\partial S}\right)$$ and $S$ is defined as $$S = k_B \ln \Omega$$ where $\Omega$ is the number of accessible states of the system for a given ...
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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 ...
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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. ...
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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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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 ...
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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 $\rho_0=\frac{1}{Z}e^{-\beta H}$ ...
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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 ...
12
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Bekenstein entropy black hole v.s Hawking entropy black hole

Historically, Bekenstein estimated the entropy associated with a black hole in 1973, obtaining: $$ S_B = \frac{\ln(2)k_Bc^3}{8\pi\hbar G}A. $$ He already acknowledges in his article that his estimates ...
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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. ...
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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?
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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) ...
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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 ...
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Intuitive understanding of the definition of entropy

In Wikipedia, the definition of entropy goes like this: $ d S = \dfrac{\delta q_{\rm }}{T}$. The literal interpretation of this equation is that some amount of heat transferred into a system, if the ...
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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 ...
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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 $q$ ...
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Motivation for the use of Tsallis entropy

Every now and again I hear something about Tsallis entropy, $$ S_q(\{p_i\}) = \frac{1}{q-1}\left( 1- \sum_i p_i^q \right), \tag{1} $$ and I decided to finally get around to investigating it. I haven't ...
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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 ...
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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 ...
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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 ...
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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 ...
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465 views

How do you prove the second law of thermodynamics from statistical mechanics?

How do you prove the second law of thermodynamics from statistical mechanics? To prove entropy will only increase with time? How to prove? Please guide.
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Will entropy continue to increase even if the universe begins to contract?

If the universe is heading for a big crunch, when the universe starts to collapse will entropy decrease and the arrow of time consequently reverse or not? I'm interested in the explanations, not just ...
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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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184 views

Why does $S = k_B \ln W$ not always apply?

I thought for a long time that the Boltzmann formula for entropy, $S = k_B \ln W$, was a universally true statement, or rather the definition of entropy from the perspective of statistical mechanics. ...
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Perpetual motion machine of the second kind possible in nano technology?

First of all sorry for my English - it is not my native language. During my engineering studies at the university the thermodynamics professor told us that the "second law of thermodynamics is not ...
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Definition of the 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 ...
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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 ...
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How is information related to energy in physics?

I recently attended a talk by Dr. Ravi Gomatam on 'quantum reality', where the speaker suggested, that conservation of energy is not a fundamental law, and is conditional, but the conservation of ...
7
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Information Preservation and Burning Books

I recently read an article in the NY Times called A Black Hole Mystery Wrapped in a Firewall Paradox. I really liked the article, but reading one quote immediately made me think of asking Physics.SE a ...
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Casimir effect as an entropic force

When I first learned about the depletion interaction, my initial reaction was that it looks very similar to the Casimir effect. On making this remark to the professor, he replied somewhat mystically: ...
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Entropy of the Sun

Is it possible to measure or calculate the total entropy of the Sun? Assuming it changes over time, what are its current first and second derivatives w.r.t. time? What is our prediction on its ...
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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 ?
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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 ...
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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: ...
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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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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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Can entropy be equal to zero?

I've searched for it but I only found contradicting answers from "scientists": Dr. David Balson, Ph.D. states: "entropy in a system can never be equal to zero". Sam Bowen does not refutes the ...
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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 ...
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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 ...
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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 ...
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Can entropy of Universe be constant?

If I understand entropy correctly, then for example two objects orbiting a centre of mass have lower entropy than when said objects eventually crash into each other and form a new one. So let's say ...
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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 ...