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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366 views

What is the entropy of the universe today?

What's the entropy of the universe today? How does one go about calculating this? I've heard the statement that black holes account for the bulk of the entropy in the universe today, but don't know ...
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322 views

Bekenstein entropy black hole v.s Hawking entropy black hole

Historically, Bekenstein estimated the entropy associated with a black hole in 1973, obtaining: $$ S_B = \frac{\ln(2)k_Bc^3}{8\pi\hbar G}A. $$ He already acknowledges in his article that his estimates ...
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1answer
127 views

Free Energy, Avialable Work in a reversible process

I was reading the Wikipedia page on Helmoltz Free Energy, http://en.wikipedia.org/wiki/Helmholtz_free_energy, and run across a point I cannot unravel. The discussion goes as follows, I reproduce it ...
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0answers
85 views

Could CP violation be exploited to violate the second law?

I don't understand well CP-violation, but since it introduces a microscopic irreversible process, couldn't it be somehow exploited to decrease entropy? For instance, if we could somehow use it to bias ...
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1answer
361 views

Entropy in biological systems

I understand why entropy tends to a maximum; it is the tendency of a system to spend most of its time in the macroscopic state that corresponds to the largest number of phase cell configurations. How ...
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3answers
706 views

Mathematical proof of non-negative change of entropy $\Delta S\geq0$

I understand that we can prove that for any process that occurs in an isolated and closed system it must hold that $$\Delta S\geq0$$ via Clausius' theorem. My question is, how can I prove this in a ...
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1answer
199 views

Immediately after the Big Bang, was the universe in a state of extremely low or extremely high entropy?

Phase space theory suggests that the largest course-graining region, $p$, in a phase space, $P$, is the point in the phase space with the highest entropy. As such, it is in thermal equilibrium with ...
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2answers
122 views

What is the effect of phase transition on the thermodynamic state variables of a material?

When a material undergoes a phase transition, it releases an amount of heat (under a specific temperature). So the effect of the phase transition on entropy would be equal to: \begin{align} ...
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2answers
406 views

Statistical Entropy and Information theory

I am having trouble in understanding the following concepts : Pg 231 Appendix B of the link ...
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0answers
71 views

Entropy bounds and the size of the universe

The principle that the maximum amount of information or entropy a volume of space can hold is proportional to its surface area apparently applies to all space, not just black holes. Since volume grows ...
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1answer
133 views

Definition of entropy

In my textbook there is written $$\Delta S = \int_R \frac{\delta Q}{T}$$ where the $R$ means calculated along a reversible transformation. The variation of entropy only depends upon the ...
2
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1answer
159 views

Is there a standard reference where entropy is set equal to zero in property tables?

For practical considerations, it seems that entropy is only meaningful as a difference between states, like $\Delta s$ going from state A to state B. For an ideal gas, for instance, standard formulas ...
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67 views

entropy relation between ads$_2$ black hole and near extremal ads RN black brane

It seems that the entropy for AdS$_2$ black hole is independent of the temperature $s=s_0$. While for near extremal AdS RN black brane, $s=s_0+ s(T/\mu)$. Should not these two entropies be the same ...
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0answers
390 views

Entropic force in polymers

According to my textbook, the elastic force in a rubber is caused to the tendency of the polymers to return to their initial disordered state of higher entropy. But isn't this looking at entropy on ...
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3answers
2k views

Does evaporation decrease entropy?

I have a container of water in thermal equilibrium (there are no temperature fluctuations inside the container). Some molecules will evaporate out of the container of water thus decreasing its ...
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2answers
331 views

Inequality of Clausius

I'm having some trouble understanding the inequality of Clausius. My treatment of the inequality applies to an engine operating in a cycle between two temperatures (i.e. like a Carnot engine). The ...
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1answer
109 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 ...
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1answer
69 views

Calculating energy U from $\partial U/\partial q$

Imagine $N$ oscillators with only two possible energies, $\epsilon_0$ and $ \epsilon_1$, with $\epsilon_1 > \epsilon_0$. Taking $\epsilon_0 = 0$ for now I showed $\Omega(q\epsilon_1) = ...
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1answer
341 views

An explanation for the Landauer's principle

Has anyone understood the Landauer's principle? What is the current status? In specific, is there a theoretical derivation of the Landauer's Principle?(not the heuristic one based on Salizard's ...
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1answer
128 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 ...
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1answer
50 views

Status of time in a Universe at maximum entropy

In billions and billions (thanks Carl Sagan) of years I have heard that atoms will lose energy and their temperature will approach absolute zero and thus their entropy will approach a minimum level. ...
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2answers
248 views

While holding an object, no work done but costs energy (in response to a similar question)

I read the answer to Why does holding something up cost energy while no work is being done? and wanting to know more, I asked my teacher about it without telling him what I read here. Instead of ...
2
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1answer
97 views

Details in the derivation of the second law starting from the phase space volume

I had a question on one of the details of the derivation of the second law of thermodynamics starting from the phase space volume. I'll type out what I understand so far: Letting the Hamiltonian ...
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3answers
716 views

Does entropy apply to Newton's First Law or does “acted upon” always require an external factor?

First law: Every body remains in a state of rest or uniform motion (constant velocity) unless it is acted upon by an external unbalanced force. This means that in the absence of a non-zero net ...
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2answers
201 views

Can entropy of a system decrease if we wait long enough?

A ball rests on a smooth surface. The ball's particles are in constant motion. So are the particles of the floor. Some of the ball's particles collide with the floor's particles and transfer kinetic ...
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15k views

Can entropy be equal to zero?

I've searched for it but I only found contradicting answers from "scientists": Dr. David Balson, Ph.D. states: "entropy in a system can never be equal to zero". Sam Bowen does not refutes the ...
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2answers
144 views

Backward Time Flow?

Physicists say that time is moving foward because entropy always increases. But have physicists considered that we might be mistaken? Since there is no ultimate reference frame, it could be possible ...
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98 views

Is the black hole surface area actually zero?

From quantum mechanics we know that entropy of a part can be smaller than the entropy of the whole. I wonder whether a similar rule works for GR as well. Quantum mechanics predicts that the entropy ...
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4answers
265 views

Does entropy alter the probability of independent events?

So I have taken an introductory level quantum physics and am currently taking an introductory level probability class. Then this simple scenario came up: Given a fair coin that has been tossed 100 ...
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1answer
176 views

How to reconcile these two principles?

Quantum mechanics says that the entropy of an unobserved system remains constant. As such, the apparent growth of entropy is a subjective illusion. If we consider the wave function of the universe, ...
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1answer
705 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 ...
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295 views

Does natural unit of information and entropy, nat, play special role in the freebit picture?

Please refer this question to understand why I consider the freebit picture important. In short, it is conjectured, that for certain real systems the most complete physical description possible ...
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5answers
3k views

Is a world with constant/decreasing entropy theoretically impossible?

I'm not 110% sure exactly what I mean by this question. It was sparked by a friend who said he wished the law of entropy were reversed, so he wouldn't have to worry about cleaning the bathroom. ...
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1answer
168 views

Would not gravity negate entropy?

Back in high school, I asked my teacher gave us a quick explanation of relativity. Specifically, he told us what $E=mc^2$ meant. He explained that, at least as far as we needed to be concerned, matter ...
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1answer
60 views

Maximising entropy when energy is shared between systems

This is a problem to do with statistical physics, and the exchange of energy when we have two microcanonical ensemble. I don't understand why there should be a minus sign in the middle, if Energy* ...
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1answer
203 views

Information content of the expanding Universe

As I understand, in physics, 'information' is closely tied to thermodynamic entropy. Does this relationship imply that if the Universe expands and ends in 'heat death' (maximum entropy?) that it ...
3
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1answer
659 views

Connection between Kolmogorov entropy and Boltzmann entropy

http://math.stackexchange.com/questions/527384/what-is-the-connectivity-between-boltzmanns-entropy-expression-and-shannons-en mentions a relationship between Shannon entropy and Boltzmann entropy. Is ...
2
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2answers
176 views

Bolzmann entropy [duplicate]

The Boltzmann entropy is defined as the logarithm of the phase space volume (E). Is there a reference, book, paper which shows where this definition comes and how it is equal to the phase space ...
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1answer
56 views

An isolated Earth

It is known the fact that there is no way to extract energy (in any form) from any system without introducing some energy. The Earth for example, gets energy from the Sun, from nuclear fusion of ...
2
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2answers
181 views

Entropy difference between initial and final states for a spherical photon cell collapsing in a black hole

Consider a spherical symmetric thin cell of photons converging to a point. At some moment, there is a formation of an horizon and a black hole. But each black hole is evaporating,and so, after some ...
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1answer
141 views

Entropic force in rubber bands [closed]

The formulation for entropic force of stretching a rubber band is now known. Are there any other such daily life examples that also have mathematical formulations of entropic forces associated with ...
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1answer
178 views

What is the probability of ice in boiling water?

Ice crystals are spatially ordered, and in every randomness there is a low possibility of temporarily order. If given enough boiling water, and sufficient time, could local clusters water molecules ...
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1answer
497 views

How does this argument imply that entropy does not change in a quasi-static adiabatic process?

I am working through some notes of Gould and Tabochnik here and I am confused by their argument showing that entropy does not change in a quasi-static adiabatic process. First, entropy is defined to ...
7
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0answers
217 views

Significance for LQG of Sen's result on entropy of black holes?

Sen 2013 says, ...we apply Euclidean gravity to compute logarithmic corrections to the entropy of various non-extremal black holes in different dimensions [...] For Schwarzschild black holes in ...
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1answer
87 views

Would the universe get consumed by blackholes because of entropy?

Since the total entropy of the universe is increasing because of spontaneous processes, black holes form because of entropy (correct me if I'm wrong), and the universe is always expanding, would the ...
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1answer
111 views

Mixed quantum states and “complete knowledge of the system”

I ran across this statement in a professor's notes and I think it's just a typo, but I wanted to take the opportunity to check my understanding. So in his notes it says: even if we have complete ...
2
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3answers
661 views

What is the relationship between the second law of thermodynamics and evolution?

On one hand evolution seems to drive against the second law in that it creates a state of (locally) higher order. On the other hand the second law seems to drives evolution - in the sense that it ...
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1answer
325 views

How do you define a reversible path for general processes?

The equation $dS = \frac{\delta Q}{T}$ is only defined for a reversible path. Given a irreversible path we typically calculate the entropy by choosing a reversible path from the same initial to final ...
2
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1answer
54 views

Experiment dropping electrons into glass of protons

So, when you drop dye into a glass of water the dye spreads out. Now I realize you cant simply replace the water in the glass with protons (or a pure concoction of electrons) but I am wondering... ...
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1answer
1k views

Why the dissolution of hydrophobic compounds decreases the entropy of water molecules in the vicinity of the solute?

The following is a quote from Lehninger's Principles of Biochemistry, 4th edition, pg.52: (...) dissolving hydrophobic compounds in water produces a measurable decrease in entropy. Water ...