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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Von Neumann entropy of mixtures of coherent states

I'm trying to calculate the Von Neumann entropy of statistical mixtures of coherent states. The problem is that such states are in general non-Gaussian, so one cannot follow the formalism developed ...
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129 views

Do gravitational waves have entropy?

We know, according the current understanding of black holes and General Relativity, as well as quantum fields in General Relativity, that black holes have an entropy proportional to the area of the ...
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11 views

Relationship between entropy and Lyapunov exponent

If $\lambda$ is the largest positive Lyapunov exponent of a piecewise linear dynamical chaotic discrete in time map, then is there a relationship between the entropy and its $\lambda$. I remember ...
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30 views

A system with temp T is in contact with a reservoir of temp T. Would the system ever take in energy and expand (do work) in this situation?

The context is explain a Carnot cycle and how to get work from a system. Its starts by saying the system is in equilibrium with its surroundings, but then it take in some energy Qin. How does ...
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1answer
34 views

Why does stagnation pressure reduce across a normal shock?

I am seeking an explanation for this graph where the subscript "1" refers to the supersonic region and the subscript "2" refers to the subsonic region present beyond a normal shock. The static ...
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78 views

Entropy of unattended music streaming and other useless processes

I just realized that on my work pc, I had an internet music streaming service turned on for the last week, but muted (=useless). I was wondering how much entropy in excess was generated by ...
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Understanding Gibbs $H$-theorem: where does Jaynes' “blurring” argument come from?

According to this Wikipedia article, the $H$-theorem was Boltzmann's attempt to demonstrate the irreversible increase in entropy in a closed system starting from reversible microscopic mechanics. ...
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25 views

Collapse of two large black holes in AdS

In $4d$ flat space, two black holes of mass $M$ can collapse to form another one of (roughly) mass $2M$. This process is spontaneous, as reflected by the fact that the black hole entropy $S=M^2$ ...
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621 views

Entropy and Information

Several posts and my classes in thermodynamics equate increase in entropy with loss of information. Shannon clearly showed that the information content of a message is zero when its entropy is zero ...
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48 views

Intelligence and Entropy [closed]

Is intelligence an entropy transformer? and the difference between a lower and higher intelligence is the efficiency?
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58 views

Can black holes grow via accretion of dark matter particles?

I'm assuming that the answer to the question in the title is a resounding yes. Since Baryonic matter and dark matter interact via gravitational forces. If this is the case how is information not lost ...
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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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What has a greater effect on Entropy, number of molecules or volume of container? [closed]

As the number of molecules in a system increase, so do the number of possible microstates, and therefore entropy does as well. Similarly, the more room you give a set number of molecules to move in, ...
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179 views

How does entropy change when heat is transfer into a system reversibly with constant $T$?

My guess will be $\Delta S_\mathrm{(system)}$ : increase [because heat is flowing into the system] $\Delta S_\mathrm{(surrounding)}$: decrease [because heat is leaving the environment] $\Delta ...
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4answers
103 views

Is it possible for a system to become irreversible?

Imagine a ball bouncing in a box for a long time. We know, there is a certain path it can go to bounce off infinitely (see the image). If it gets to this state, it will never be able to get back ...
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3answers
127 views

Does entropy always increase with temperature? [duplicate]

For any system can we always say that entropy increases with temperature. In other words: $$\left(\frac{\partial S}{\partial T} \right)_{\{\alpha\}}\ge0$$ where $\{\alpha\}$ is the set of parameters ...
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78 views

The calculation of the entropy of a single atom

I used to think that the entropy of a single atom could not be calculated, for in my mind only the entropy of a system containing many atoms could be calculated. But my professor told me the entropy ...
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369 views

If entropy is a state function, then why is all the talk about reversible vs. irreversible processes?

So I'm preparing for my Thermodynamics undergrad exam, and I just can't wrap my head around the significance of reversibility vs. irreversibility of a process in relation to entropy. I mean if entropy ...
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1answer
278 views

Does the radius of the Universe correspond to its total entropy?

I heard a claim that due to holographic principle, the surface area of the cosmic horizon corresponds to the universe's total entropy. As such the initial state had zero surface area and later ...
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1answer
59 views

If Black holes are maximal entropy how can they evaporate?

According to Hawking/Bekenstein a black hole represents the highest amount of entropy for a given volume, (actually the entropy is related to the surface area of the black hole but the fact that they ...
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Entropy always increases in a closed system - what if the universe is open?

An interesting question I was asked: Entropy always increases in a closed system - what if the universe is open? Does that mean that entropy can decrease in such a system? Of course, I think there is ...
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42 views

Entropy and vacuums

If I have a vacuum (completely devoid of any particles; Q.M. effects aside), then turn a nozzle and let a gas freely expand into the vacuum, will I have increased the entropy of the vacuum? I get ...
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0answers
35 views

Gravitational entropy [duplicate]

In the beginning (big bang), mass was evenly distributed (if you consider an elementary particle as an extended object, like a circle on a very thin cylinder, with a radius near the Planck length, but ...
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3answers
94 views

What ds>dQ/T mean?

I read the derivation on page 216 over here: https://www3.nd.edu/~powers/ame.20231/notes.pdf First it considers an irreversible process between state 1 and 2 followed by a reversible process between ...
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1answer
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Entropy for $N$ number of particles [closed]

If there are $N$ number of non-interacting and distinguishable particles which have either Energy $E_1$ or $E_2$ , then a. What will be the entropy $S(n)$ for such system? ($n$ is the number ...
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2answers
49 views

Increase in entropy principle

If we consider a system to undergo an irreversible process from state 1 to state 2 and a reversible process from state 2 to state 1, then through Clausius inequality $\int_{1}^{2} \frac{\delta ...
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Extensiveness of entropy in classical microcanonical ensemble

In introducing microcanonical ensemble of classical statistical mechanics one pretty much starts by postulating that entropy of the system has the form $S(V,E) = k \log \Gamma(V,E)$, where $\Gamma$ ...
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35 views

What processes create or destroy information?

From a classical standpoint, it seems pretty clear that information can be easily lost. If you knock over a bookshelf and the books fall out, it seems like their initial order on the shelf cannot be ...
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Can the second law of thermodynamics be violated in a small enough system if tried repeatedly enough?

Second law of thermodynamics is observed in the universe because statistics favors it, right? And in large enough system this statistical tendency becomes certainty. Does it also mean that negative ...
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185 views

Why doesn't the separation of particles by mass via gravity decrease entropy?

Let's say we've got a fluid of heavy and light particles inside a cubical flask, which is initially shaken up so that the density of heavy particles is uniform everywhere. Let's also say that these ...
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525 views

Definition of entropy in thermodynamics

In most textbooks, the definition of entropy in reversible processes on a system $S$ is given simply as $$d S=\delta Q/T.$$ It seems to me this definition is insufficient since it does not specify ...
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2answers
34 views

Why does hot water gets cooler on stirring instead it should have gotten hotter

When we keep on stirring hot water vigorously it starts getting cooler. But we are increasing the random kinetic energy of the molecules of water. Heat is as it is the energy of RANDOM motion of ...
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3answers
200 views

Is Bekenstein entropy limit inconsistent with universal continuity?

It is unknown whether the universe is discrete or continuous in its intricate quantum level structure. See for example: Can universal continuity be experimentally falsified? Is the universe finite ...
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1answer
35 views

Is there a way to prove information entropy?

Information entropy is a very general term involving everything from the tendency of material to decay (in all the 3 meanings) to the fact that you need energy to sort your books alphabetically. ...
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132 views

At an instant, does a system of gravitational charges exhibit equivalent behavior to a time-reversed system of like electric charges?

Question: In principle, does a system of gravitational charges exhibit equivalent behavior to a time-reversed system of like electric charges? (At a single instance in time?) Additional Notes: I am ...
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386 views

Why is entropy an extensive quantity?

If we have two identical isolated macroscopic systems both with energy $E$. The number of accessible states of each of them is $\Omega(E)$ and hence the entropy is $\ln\Omega(E)$. Now if we put them ...
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Why is heat transfer reversible when temperature difference is infinitesimal?

I don't understand why heat transfer from hot reservoir to the system is considered reversible in this case: $T_{reservoir}$ = $T_{system}$ + dT but it's considered irreversible in this case: ...
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240 views

Entropy change in an irreversible process between 2 equilibrium state

Calculating entropy change in an irreversible process between 2 states requires computing the change in entropy for any reversible process between the 2 same states, but why? If someone could provide ...
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1answer
84 views

How to justify the entropy maximum postulate using Statistical Mechanics?

The entropy maximum postulate states that given a thermodynamic system there's a function $S$ of the extensive parameters called entropy which has the property that once a constraint is removed the ...
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1answer
130 views

Why don't we observe spontaneous symmetry restoration in nature?

Why do we always observe spontaneous symmetry breaking in nature and not restoration? Does there exist some argument with the 2nd law of thermodynamics and the entropy of the universe increasing? If ...
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23 views

Is perfectly diffuse reflection entropy maximizing?

Suppose that I shine light on a surface and none of it will be absorbed or transmitted, and the spectrum doesn't change (so that all that's left to determine is the power reflected from the surface as ...
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1answer
78 views

If an object has a temperature, does it have to radiate?

I'm reading through a powerpoint presentation about Hawking Radiation (HR). They are explaining all of the reasons that built up to the postulate of HR, and one of the reasons is that if there is a ...
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60 views

Holevo Information and Quantum Mutual Information

This question is about the difference between Quantum Mutual Information and Holevo Information of quantum channels. From http://arxiv.org/pdf/1004.2495.pdf equation 7 we know that the sum of quantum ...
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1answer
37 views

Why can't an ocean liner be powered by an engine that takes heat from the ocean water and eject ice cubes?

The following excerpt comes from the physics textbook Understanding Physics, by David Cassidy, Gerald Holton, and James Rutherford: A ball lying on the floor will not somehow gather energy from ...
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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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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 ...
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5answers
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Difference between heat capacity and entropy?

Heat capacity $C$ of an object is the proportionality constant between the heat $Q$ that the object absorbs or loses & the resulting temperature change $\delta T$ of the object. Entropy change is ...
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7answers
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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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Is entropy absolute (as in absolute temperature)?

Following this question on the Entropy at the Big Bang where I asked: Since Entropy always increases (in general); its expected that the entropy at the beginning of the universe should be the ...
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What are the phenomena responsible for irreversible increase in entropy?

https://www.quantamagazine.org/20140416-times-arrow-traced-to-quantum-source This article says that entanglement drives the arrow of time of increasing entropy towards thermodynamic equilibrium: ...