# Tagged Questions

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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### 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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### 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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### 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 ...
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### 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 ...
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### 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 ...
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### 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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### 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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### 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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### 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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### 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 ...
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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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? ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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 ...