A important extensive property of all systems in thermodynamics, statistical mechanics, and information theory, quantifying their disorder (randomness), i.e., our lack of information about them. It 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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Where is the flaw in this machine that decreases the entropy of a closed system?

I was thinking about a completely unrelated problem (Quantum Field Theory Peskin & Schroeder kind of unrelated!) when the diagram below sprang into my mind for no apparent reason. After some ...
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What is information?

We're all familiar with basic tenets 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 indestructible?

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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Is there a thermodynamic limit on how efficiently you can solve a Rubik's cube?

Suppose I build a machine which will be given Rubik's cubes that have been scrambled to one of the $\sim 2^{65}$ possible positions of the cube, chosen uniformly at random. Is it possible for the ...
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Homemade salad dressing separates into layers after it sits for a while. Why doesn't this violate the 2nd law of thermodynamics?

The oil, vinegar and other liquids in homemade salad dressing separate into layers after sitting for a while, making the mixture become more organized as time evolves. Why doesn't this violate the ...
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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 ...
28
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871 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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Where does deleted information go?

I've heard that, in classical and quantum mechanics, the law of conservation of information holds. I always wonder where my deleted files and folders have gone on my computer. It must be somewhere I ...
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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 ...
23
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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 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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Entropy is…disorder?

As I read somewhere, it said that the universe is heading toward disorder a.k.a entropy increasing. Now as far as I know from the second law of thermodynamics it states that entropy is indeed ...
22
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Will the black hole size increase?

I was thinking about the following thought experiment, but wasn't sure about its outcome. Suppose there is a black-hole and I enter it with a partitioned box containing two different gases on either ...
21
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894 views

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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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. ...
18
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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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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 ...
17
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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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What was the entropy of the universe at the time of the Big Bang?

(I asked this question in Philosophy.SE; but I was advised to direct it here, despite it is, in my opinion, somewhat too speculative for physics.SE). High entropy generally means high disorder; and ...
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Why doesn't the entropy increase when two similar gases mix with each other?

Entropy increases when two substances mix with each other. For example, the entropy of mixing of two different gases are given by $$\Delta S= 2Nk\ln\frac{V_f}{V_i}\;.$$ But, the entropy doesn't ...
16
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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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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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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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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 ...
15
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Why don't photons split up into multiple lower energy versions of themselves?

A photon could spontaneously split up into two or more versions of itself and all the conservation laws I'm aware of would not be violated by this process. (I think.) I've given this some thought, and ...
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What is the entropy of a pure state?

Well, zero of course. Because $S = -\text{tr}(\rho \ln \rho)$ and $\rho$ for a pure state gives zero entropy. But... all quantum states are really pure states right? A mixed state just describes ...
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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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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 ...
14
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How does dark matter collapse?: Entropy considerations

Inspired by this question. I believe that the usual explanation that preserves the second law of thermodynamics as an astrophysical gas cloud collapses under gravity is that the gas must heat and ...
14
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312 views

Doesn't entropy increase backwards in time, too?

In statistical explanations of entropy, we can often read about a (thought) experiment of the following sort. We have a bunch of particles in box, packed densely in one of the corners. We assume some ...
14
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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 ...
14
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418 views

Is the flatness of space a measure of entropy?

This is a bit quirky: For a very long time I've found Stephen Hawking's evaporating small black holes a lot more reasonable and intuitive than large black holes. The main reason is that gravity is ...
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How does the heat death looks like from inside the system?

As this answer points out, any human would first freeze rather than experience the heat death. However, assuming hypothetically that we could make some robot live at such low temperature (or even ...
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Why is entropy additive?

Although it seems simple, I can't get the derivation correct. Here is my reasoning: $P(S)=P(A)P(B)$ Where P is the probability and S, A, and B denote different systems. $S_A=-P(A)\ln P(A)$ and ...
13
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611 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) ...
13
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455 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 ...
13
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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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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 ?
12
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Is this thought experiment violating the the Second Law of Thermodynamics?

There is an adiabatic box, with a board in the middle, which is adiabatic too.The board separates the box into two parts and there is a small hole in it, which is close to a coil and the hole has a ...
12
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871 views

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 ...
12
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321 views

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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What is entropy really?

On this site, change in entropy is defined as the amount of energy dispersed divided by the absolute temperature. But I want to know: What is the definition of entropy? Here, entropy is defined as ...
11
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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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Why does heat added to a system at a lower temperature cause higher entropy increase?

Entropy is defined in my book as $\Delta\ S = \frac{Q}{T}$. To derive the formula it says that entropy should be directly proportional to the heat energy as with more energy the particles would be ...
11
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Entropy increase vs Conservation of information (QM)

Unitarity of quantum mechanics prohibits information destruction. On the other hand, the second law of thermodynamics claims entropy to be increasing. If entropy is to be thought of as a measure of ...
11
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2answers
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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 ...
11
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Does electricity have an associated entropy?

One can certainly measure entropy changes associated with the generation of electricity, but does electricity itself have an associated entropy (maybe related to voltage, current etc.)?
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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 ...
11
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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 ...