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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403 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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11answers
8k views

What is entropy really?

On this site, change in entropy is defined as the amount of energy dispersed divided by the absolute temperature. But I want to know: What is the definition of entropy? Here, entropy is defined as ...
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0answers
40 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 ...
1
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2answers
119 views

Free expansion of an ideal gas

I am having trouble understanding the transient phase of an ideal gas expanding into vacuum. Firstly, the pressure of any gas is defined only when there is an instrument (barometer/ wall/ piston) ...
3
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1answer
49 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
690 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." ...
4
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1answer
229 views

Proving that Measurement increases von Neumann entropy [on hold]

Let $V$ be a finite dimensional complex inner product space. Let $\mathcal{M}$ be the classical sample space of measurement outcomes that may occur in a given experiment, and $M_\mu$, $\mu \in \...
30
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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 ...
0
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1answer
83 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&...
1
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2answers
120 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!
1
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2answers
161 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? ...
0
votes
1answer
201 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 S_\...
0
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1answer
105 views

Does a venturi injector contradict the 2nd law of thermodynamics?

The picture below shows a venturi injector. When the water flow enters the narrower cross section its velocity increases and its pressure decreases. Subsequently, fluid is sucked (or injected) into ...
1
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1answer
1k views

How does the entropy change during the cooling of a hot coffee in a cold cup?

The second Law of Thermodynamics states that entropy always increases in the universe: things become more disorganised. This means, that if I have a hot coffee in a cold cup, then the heat will ...
1
vote
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 ...
21
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5answers
7k views

Is there any proof for the 2nd law of thermodynamics?

Are there any analytical proofs for the 2nd law of thermodynamics? Or is it based entirely on empirical evidence?
0
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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 ...
4
votes
2answers
752 views

About Boltzmann H-theorem

What is the assumption for Boltzmann H-theorem? One can derive it just from the unitarity of quantum mechanics, so this should be generally true, does it imply a closed system will always thermalize ...
0
votes
1answer
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 ...
0
votes
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 ...
3
votes
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}{\...
3
votes
1answer
198 views

Entropy of the cosmological constant and the laws of thermodynamics?

Convention The convention being used is: $ A_{C} = $ The classical variable Premise Consider the following toy-model universe: A universe with a positive cosmological constant. Basic ...
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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 ...
2
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2answers
55 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 ...
1
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1answer
120 views

Meaning of the Reduced Density Operator

I am confused about what it is exactly that a reduced density operator describes. To illustrate, I came across the following seemingly paradoxical argument. Consider a bipartite system $AB$, ...
13
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2answers
640 views

Black hole no-hair theorems vs. entropy and surface area

I was revisiting some old popular science books a while ago and two statements struck me as incompatible. No-hair theorems: a black hole is fully-described by just a few numbers (mass, spin etc) ...
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4answers
3k views

How do you prove $S=-\sum p\ln p$?

How does one prove the formula for entropy $S=-\sum p\ln p$? Obviously systems on the microscopic level are fully determined by the microscopic equations of motion. So if you want to introduce a law ...
2
votes
2answers
267 views

Maxwell's Demon bug, trapdoor space and time

What about the size of the door (space) and how long has it to be opened (time)? I think Maxwell's demon would have a problem with space, if the door is too wide (more than one particle size), then ...
18
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6answers
2k views

Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution?

Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution? I have never seen dissipation explained, although what I have seen a lot is descriptions of ...
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 ...
1
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2answers
506 views

Why doesn't this violate the 2nd law of thermodynamics?

Consider an ideal gas in a cylindrical container in a gravitational field, with a piston on top pushing down by gravity. The piston has some locking mechanism that locks it in place if it is displaced ...
1
vote
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 ...
10
votes
3answers
2k views

Maxwell's Demon Constant (Information-Energy equivalence)

New Scientist article: Summon a 'demon' to turn information into energy The speed of light c converts between space and time and also appears in $E=mc^2$. Maxwell's Demon can turn information ...
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1answer
137 views

Entropy and probability

I read "The NEW world of Mr. Tompkins" and I'm not sure with one of the Gamow's equation. When he calculated the probability of entropy, he used this reasoning: "How likely is a situation that all the ...
4
votes
3answers
3k views

What is the meaning of Boltzmann definition of Entropy?

I would like to ask if someone knows the physical meaning of Boltzmann's definition of entropy. of course the formula is pretty straightforward $$S=k_b\ln(Ω)$$ but what in the heck is the natural ...
2
votes
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 ...
2
votes
3answers
266 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 ...
1
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1answer
118 views

free energy and entropy

my understanding of free energy and entropy is that as entropy of a system increases its free energy decreases. As sun has free energy and this energy is being converted to useful work, and its ...
14
votes
2answers
325 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 ...
1
vote
1answer
101 views

Reversible cycle approximated by Carnot cycles

My textbook, W.E. Gettys, F.J. Keller, M.J. Skove, Physics 1, gives the definition of a reversible transformation as a transformation that can be inverted by effectuating only infinitesimal changes in ...
7
votes
5answers
573 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 ...
7
votes
3answers
149 views

Arrow of time and entropy?

The arrow of time is usually defined by the direction in which entropy increases. In a closed system, if there's a max entropy that the system can reach, does that mean time stops or at least become ...
4
votes
1answer
149 views

A mass falls to the ground from a height. What's the change of the entropy of the universe?

A mass $m$ falls to the ground from a height $h$. The temperature $T$ is constant. What's the change of the entropy of the universe? It's an example in Carter's Classical and Statistical ...
5
votes
5answers
438 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. ...
2
votes
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 ...
79
votes
3answers
5k views

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 ...
17
votes
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 ...
4
votes
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
votes
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 ...
20
votes
7answers
1k views

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 ...