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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Why do socks in a ball separate in the washing machine?

When I take a pair of socks off I bundle the two socks together into a ball. I then put many pairs into the washing machine and when the cycle is finished they are all separated. For me to ...
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3answers
108 views

Is this explanation for the Universe's low entropy at its origins plausible? [on hold]

I've been thinking about this, and it may sound very ludicrous (and it probably is), but I may have come up with a proto-explanation for it. I hope I won't come across as some misinformed perpetual ...
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1answer
52 views

Why is black hole entropy not an extensive quantity?

The Bekenstein entropy for a black hole is proportional to the surface area $A$ of the black hole $$ S_{BH} = \frac{k_B}{4 l_P} A $$ with the Planck length $l_P = \sqrt{\frac{\hbar G}{c^3}}$. The ...
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0answers
43 views

What is a maximally entangled state? Or better, what really is entanglement entropy?

I was trying to understand the concept of entanglement entropy and for that I was studying the density operator formalism in the context of a bipartite quantum system. In some references, people ...
3
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0answers
62 views

Proving that the Boltzmann entropy is equal to the thermodynamic entropy

I've been trying to understand how we can equate the Boltzmann entropy $k_B \ln \Omega$ and the entropy from thermodynamics. I'm following the approach found in the first chapter in Pathria's ...
3
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1answer
54 views

Which temperature does $T$ in Clausius inequality ($\oint \frac{\delta Q}T\le 0$) refer to?

I got a little confused about the temperature in Clausius inequality. As you can see in this answer of Luboš Motl, it seems that temperature is the temperature of the system. But in some answers of ...
3
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2answers
713 views

Is the reciprocal of Entropy easier to understand? [on hold]

"A thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system." ...
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3answers
2k views

How much mass can colliding black holes lose as gravitational waves?

Concerning the recent detection of gravitational waves produced by colliding black holes, it has been reported that a significant percentage of the combined mass was lost in the resulting production ...
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2answers
122 views

Please explain entropy curve [closed]

I saw this curve at a website, but I didn't understand it. What is the lower point of entropy, and what are the points A, B, and C? Thanks!
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1answer
41 views

Avoiding a Divide by Zero with Absolute Entropy

I've been reading that unlike enthalpy, entropy has an absolute value that we obtain by setting it equal to zero at absolute zero temperature, but I'm having a hard time understanding how to avoid a ...
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1answer
33 views

Consideration on the total entropy variation for 2 ideal gases

Let's consider an isolated container containing a mole of an ideal monoatomic gas $A$ and a mole of a biatomic gas $B$, separated by an ideal piston (hermetic). The gases slowly exchanges heat and the ...
0
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1answer
85 views

When is ${d}\,Q=T\,dS$ not true? [closed]

Why is the first T differentiated from the second in $T\,\frac{{\rm d}\,Q}{T}$ ? So why do we use a product to express this and not just ${d}\,Q$ , which goes hand in hand with the cases where $dS&...
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39 views

Principle of Maximum Work for Different Paths

The principle of maximum work states that for any process between two states, the work done by the system is maximised for a reversible process (and heat transfer is minimised), and that the work done ...
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0answers
36 views

change in entropy constant V proof

In the justification above it is noted that dV=0 througout the process. They use the macro formula dU=TdS. How can they use this formula when dV=0 hence pV=nRT gives $$T(p)=\frac{V}{nR}p=kp$$ I mean ...
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2answers
56 views

What Postulate States Entropy must be Positive?

I've been reading the Postulates of Classical Thermodynamics, and I haven't found anywhere to be said that the Absolute Entropy of a system has to be a positive number. The third one states that the ...
3
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1answer
44 views

Heat pumps: can $COP\leq 1$ and when does $COP=\frac{1}{\eta}$ hold?

Heat pump COP is defined as $$\xi=\frac{|Q_{HOT}|}{|W|}$$ Where $Q_{HOT}$ is the heat given to the hot source. I have two linked doubts about it Under what conditions I can say that $\xi=\frac{1}{\...
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1answer
57 views

What is this entropy-related thermodynamic concept called?

I'm trying to sharpen my understanding of a thermodynamic concept. Suppose I've got an idealized building whose interior is held at 10 degrees cooler than the outside air by a heat pump that consumes ...
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0answers
20 views

Quantum Discord and entropy

I'm trying to understand certain aspects of Quantum Discord. The idea is that a quantum system might have non-classical correlations despite it not being in an EPR-like state. So the discord is ...
2
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1answer
44 views

Prove all reversible heat engines that work between just two temperatures have the same efficiency

Can someone explain this explanation to me: A completely different argument focuses on the requirement that the device only move heat at one or other of the two temperatures. Then, provided ...
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0answers
24 views

Reference: authoritative reference on Gibbs and Boltzmann's entropy

Can someone reference a good, standard textbook on thermodynamics or quantum mechanics that explicitly states the formula for Gibbs and Boltzmann's entropy (or maybe Shannon as well)? I am asking ...
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5answers
440 views

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. ...
4
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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 ...
0
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1answer
45 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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2answers
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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3answers
1k views

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
62 views

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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2answers
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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2answers
57 views

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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4answers
418 views

Is information entropy the same as thermodynamic entropy?

Context In one of his most popular books Guards! Guards!, Terry Pratchett makes an entropy joke: Knowledge equals Power, which equals Energy, which equals Mass Pratchett is a fantasy comedian ...
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2answers
163 views

How to find entropy production of opening the windows in the winter?

Every time you open the windows in the winter (to bring in healthy and fresh air), room's warm air goes outside into Atmosphere. How to find entropy production of opening the windows in the winter? ...
3
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4answers
303 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 ...
0
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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
64 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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1answer
46 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
74 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: ...
0
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1answer
44 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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votes
1answer
77 views

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 ...
4
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1answer
77 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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0answers
30 views

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?
2
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2answers
99 views

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 ...
1
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1answer
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 ...
3
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1answer
64 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 ...
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, ...
2
votes
2answers
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 ...
6
votes
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, ...
2
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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 ...
3
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1answer
35 views

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 ...
6
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1answer
135 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 ...
3
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0answers
40 views

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 ...
8
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2answers
185 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 ...