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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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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46 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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81 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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94 views

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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28 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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651 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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51 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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2k 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 ?
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108 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 again....
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132 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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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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408 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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62 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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44 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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37 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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102 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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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 of ...
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57 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 Q_{...
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28 views

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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38 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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46 views

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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43 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 atoms....
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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. Let'...
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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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388 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: $T_{...
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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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133 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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26 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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82 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 ...
5
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71 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
40 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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336 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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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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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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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: ...
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A relationship between entropy and temperature

I tried deriving a formula relating entropy (not change in entropy, but entropy itself) to temperature. I’ve only seen two equations really relating to entropy thus far, and only one of them includes ...
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3answers
832 views

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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197 views

Really how does the entropy of the universe increase?

Universe means the system along with its surroundings. I have always got this statement while studying the second law; be it a thermodynamics book (Sears, Salinger) , physical chemistry book (Atkins, ...
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Is there any useful sense in which entropy fluctuates?

One of the classic distinctions between young Boltzmann and old Boltzmann was his view on entropy. Young Boltzmann had his H-theorem where a mechanical quantity H was supposed to represent entropy. ...
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About the holographic principle

I read at a book this quote "As the degrees of freedom of a particle are the product of all the degrees of freedom of its sub-particles, were a particle to have infinite subdivisions into lower-...
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102 views

Replica trick for calculating Entanglement Entropy?

This is probably a simple question. Von Neumann entropy is defined to be $$S_A=-tr_A\rho_A \log\rho_A$$. And it's said that it can be calculate from the "Replica trick": $$S_A=\lim_{n\to 1}\frac{tr_A \...
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Estimation of an Entropic Path Integral

I'm trying to reproduce some results from a paper (http://www.alexwg.org/publications/PhysRevLett_110-168702.pdf for reference) and basically I need a way of estimating a particular path integral (...
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Does the entropy of a system vary in the equilibrium?

I am not physicist and this question may seem trivial. But I understand that in the equilibrium the magnitudes such as temperature or volumen do not vary. Is the same for entropy? My logical says that ...
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3answers
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How is the efficiency of a heat engine related to the entropy produced during the process?

I'm reading Schroeder's An Introduction to Thermal Physics. Regarding heat engines, it is stated: Unfortunately, only part of the energy absorbed as heat can be converted to work by a heat engine. ...
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59 views

Entropy generation during irreversible adiabatic expansion

During irreversible adiabatic expansion entropy is generated. It means that the gas expands to as greater volume than that during reversible adiabatic expansion for the same change in pressure. How ...
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entropy changes in common processes?

Can you point me please to a reference that will explain what the entropy undergoes (increase, decrease, etc) in common thermodynamic cycle processes, like adiabatic, isobaric, isochoric, etc?
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Would it be possible that a broken glass can return to its original state spontaneous at 0K?

my teacher said that a broken glass can't fix itself spontaneous because of the second law of thermodynamics, entropy won't decrease in a isolated system. But when the temperature is at 0k, then ...