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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Change in entropy when mixing water at different temperature

Suppose two amounts of water of the same mass, but with different temperature, are mixed. Then the entropy of the hot water decreases, but the entropy of the cold water increases due to heat transfer. ...
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1answer
86 views

Entropy Change for a Thermally Isolated System

Clausius' Theorem states that $\int\frac{dQ}{T}\leq0$ for a closed cycle, with equality for a reversible cycle. Suppose we wish to take our system around a closed cycle such that the path from A to B ...
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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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Why do many people link entropy to chaos?

I understand that, in thermodynamics, entropy has a precise definition (the infinitesimal change of entropy being the infinitesimal heat transfer divided by the temperature), and that in statistical ...
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2answers
118 views

How to derive entropy from density of states?

I'm trying to derive the entropy of a black hole, given the density of states of a bosonic string (the details are not relevant). The density of states is $$ \omega(E) = E^\alpha e^{\beta E} $$ The ...
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46 views

How is a irreversible process (conventionally) represented on a $T-S$ plane and why cannot it be (really) represented?

A reversible process can be represented on a $T-S$ plane, and the area under the curve is the heat exchanged by the system. On $P-V$ plane a irreversible process is conventionally represented with a ...
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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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60 views

Relation between entropy and internal energy

I am confused as to what is the relation between entropy and internal energy. Entropy is always presented as a measure of the randomness in a system. So when we supply heat to a well insulated system ...
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1answer
475 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 ...
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227 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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Books on entropy [closed]

What books introduce entropy in a intuitive, elementary way (at most, for a person with undergraduate physics studies)? The book should not necessarily introduce entropy in relation only to ...
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83 views

Accessibility by reversible processes and the Second Law of Thermodynamics

One common way of motivating the existence of Entropy as a state function is the following. Let us take the Clausius/Kelvin-Planck statement of the second law, from which we can deduce Clausius' ...
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Change in entropy of thermodynamic environment during isobaric or isochoric processes

When an ideal gas follows a isobaric or isochoric transformation (no matter if it is reversible or not) I'm not sure what is the change in entropy of the thermodynamic environment. First of all, ...
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How did steady-state universe deal with entropy?

Until the 1960's the general consensus was that the universe is infinite years old (steady-state). The second law of thermodynamics says that entropy always increases, so we'd expect that within a ...
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Reference request for low entropy big bang

There is a somewhat widely accepted argument that the second law of thermodynamics exists because the universe began in a low-entropy state. I'm writing a paper that mentions this (and must be ...
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304 views

Why would a Boltzmann brain be transient?

The Boltzmann brain idea as I understand it: suppose the universe has an infinite lifetime. Once heat death is achieved, there are no more large-scale structures to the universe -- everything is just ...
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1answer
59 views

Entropy and Clausius inequality

From the Clausius inequality we can derive that the efficiency of a Carnot (reversible) cycle is given by: $$e= 1 - \frac{T_c}{T_h}$$ Is this true for every reversible cycle? Is the efficiency of all ...
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1answer
65 views

Does conservation of information mean that the direction of causality is arbitrary? [duplicate]

If it is the case that the information content of the universe is conserved, and the past can be constructed from a complete knowledge of the future just as easily as vice versa, then is there any ...
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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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47 views

If a flywheel is spinning at say 1,000 rpm, would an input of 500 rpm would actually slow it down? [closed]

When a flywheel is stationery, an input of 500 rpm would translate to less than 500 rpm in the flywheel considering entropy, but what happens if the flywheel is already running at 1000 rpm, wouldn't ...
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1answer
75 views

Home Work Help: Calculating Entropy for Melting Ice - Clarification on answer

The question states: What is the change in entropy for the process to completely melt 8.0 kg of ice at 0°C? The formulas for Entropy we've been introduced to are: ...
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148 views

Entropy change in a boiling egg

Yesterday in a rather intuitive Q/A session, by a visiting researcher in my town, this question got my attention.What he said was that if you boil an egg, the entropy inside the egg would increase.Now ...
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1answer
45 views

Entropy change in mixture of two gases

I'm confused about the entropy change if two gases, initially separated, are mixed togheter in a rigid box. I use the following $$\Delta S_1= n_1 c_{v,1} \mathrm{ln}( \frac{T_f}{T_{i,1}}) + n_1 R \...
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Should entropy define order rather than disorder? [closed]

Disorder, as I understand it, is basically a measure of entropy. This does not seem correct to me, and appears to be a result of our macroscopic bias. Not only does the beginning of the universe ...
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1answer
78 views

The Correct Statement of the Third Law of Thermodynamics

The Third Law of Thermodynamics can be stated in various ways, one of which is: The entropy of a perfect crystal at absolute zero is exactly equal to zero. Is this true for only "perfect ...
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What is the relationship between an expanding universe, an increase in entropy and the the creation of mass?

What is the relationship between an expanding universe, an increase in entropy and the the creation of mass? Could the creation of mass be driven by or in equilibrium with the creation of space?
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Why Boltzmann Entropy's formula is $k_B\log\ W$ and not $0.5\ k_B\log\ W$?

This question is probably wrong - however, I wish to understand even why it's wrong.. Let's take the monatomic gas situation. By the Equipartition theorem, we have that for every degree of freedom ...
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71 views

Can an adiabatic, isentropic transformation be irreversible?

My question is very similar to this, but I decided to ask another question because I felt that the problem deserved to be addressed in a more specific and formal way and I also wanted to discuss a ...
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1answer
136 views

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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1answer
65 views

As I understand it, entropy (and disorder) always increase, but gravity increases order. How does physics explain this?

Examples of ordering by gravity: The disordered cosmic dust collects into planetary systems. Planets collect the heavier elements at their cores and the lighter elements above. On Earth, iron ...
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1answer
114 views

Adiabatic piston: why is Callen's argument flawed?

This question is related to this one. I would ask you to read that question and my answer to the question itself before answering this one. The problem is the following. In his book Thermodynamics, ...
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2answers
205 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 ...
6
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1answer
58 views

How much of water's surface tension is entropic?

Water molecules on the surface of an air-water interface have preferred orientations that lower their energy. This implies that these molecules are not uniformly distributed in orientation space, ...
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75 views

Experimental confirmation of the textbook explanation for local entropy reductions

Clarification: In my original wording of this question, regrettably, I did not make it clear that I am interested in the the Boltzmann/Gibbs/statistical (BGS) interpretation of it, as opposed to the ...
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Does the Lyapunov exponent and Entropy change? [closed]

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 $\lambda$. In the paper ...
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1answer
36 views

Is Entropy Maximized, or Just Increased?

Do different real processes involve different rates of change of entropy? (Is the rate of change of entropy constant with time throughout all regions of space, or perhaps in other words, constant with ...
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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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1answer
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Effectiveness of phase-change materials vs water for heat storage?

I'm trying to understand the benefit of specialized phase-change materials vs. water for absorbing heat in a home during the day. It's my understanding that selecting phase-change materials whose ...
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2answers
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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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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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1answer
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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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1answer
55 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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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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2answers
99 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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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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678 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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1answer
54 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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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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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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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 ...