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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Mechanism of Hawking's radiation and entropy of the black hole

During Hawking's radiation, a virtual particle with negative energy and mass (from pair of particle and antiparticle) fall into black hole and its real partner having positive energy escape from ...
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2k 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 ...
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126 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
48 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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226 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 ...
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1answer
94 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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1answer
66 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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2answers
191 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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280 views

Why does $S = k_B \ln W$ not always apply?

I thought for a long time that the Boltzmann formula for entropy, $S = k_B \ln W$, was a universally true statement, or rather the definition of entropy from the perspective of statistical mechanics. ...
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141 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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97 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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1answer
79 views

do relativistic velocities change the apparent entropy content of the moving object?

Imagine a box of hot gas. It has a certain (large) amount of entropy, which we can relate to the amount of information needed to completely specify the position and velocity of every gas particle in ...
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1answer
171 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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365 views

Is this derivation of Black Hole entropy viable?

This question is motivated by this one. Suppose $l$ is the minimum measurable unit of length. What is entropy of a spinless particle contained in this interval? We know that entropy of a two-level ...
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272 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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1answer
263 views

No hair theorem and black hole entropy

The no hair theorem says that black holes rapidly converge to a state that is completely described just by their mass, spin and charge. Black hole thermodynamics says that the black hole entropy is ...
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1answer
162 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
622 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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1answer
346 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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1answer
59 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
191 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 ...
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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 ...
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2answers
171 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
590 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 ...
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364 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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78 views

Modeling a list with a tunable degree of disorder/shuffling

Imagine we have a list of ordered numbers $L = (1, 2,\dots, N)$. I want to add an arbitrary amount of "disorder" to that list. For instance: Adding a little bit of disorder would permute a few ...
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1answer
133 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
409 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 ...
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1answer
165 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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204 views

Is Information a potential or kinetic kind of energy?

It is said that the law of least action is that nature tries to convert potential energy into kinetic one as fast as possible. Information can't be thought without a physical realisation, see here. ...
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1answer
364 views

How does the internal energy and entropy depend on mass?

I've found this thermodynamics question: Given a fluid described by the following equations: $$PV^{1/3}=aT^3 ,\quad U=3aT^3V^{2/3}, \quad S=\frac{9}{2}aT^2V^{2/3}$$ The parameter $a(n)$ ...
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3answers
305 views

Natural units of information

In physics entropy is usually measured in nats. I wonder is there a possible model of a physical system which has entropy of discrete number of nats? How particles and degrees of freedom should be ...
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4answers
682 views

Is there any optical component that uniformizes the incoming light?

Is there any optical component in existence that uniformizes randomly pointing rays?
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3answers
612 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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241 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 ...
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1answer
284 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 ...
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1answer
51 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
249 views

Confusions regarding entropy

Help, I am terribly confused about entropy. On the one hand, I am taught at school that a substance such is an ice/solid has a lower entropy than its gaseous equivalent and that a process such as ...
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1answer
99 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 ...
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1answer
225 views

Can exergy and exergy destruction be understood through thermodynamical and/or statistical-mechanical principles?

My textbook Fundamentals of engineering thermodynamics, Moran and Shapiro states: The exergy is the maximum theoretical work obtainable for an overall system consisting of a system and the ...
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1answer
549 views

Entropy with infinite baths

I'm struggling with the following problem: (Stephen J. Blundell, Concepts in Thermal Physics S. 154 Problem 14.5): A block of lead of heat capacity 1kJ/K is cooled from 200K to 100K in two ...
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1answer
462 views

How certain is the heat death of the universe?

According to our current scientific knowledge, how certain is it that heat death shall be the ultimate fate of our universe, and why? Are there any serious hypotheses competing with heat death, and if ...
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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 ...
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1answer
202 views

Can anyone explain the idea behind dS ∝ dV/V?

In a lecture on entropy, one of the equations $dS ∝ \frac {dV}{V}$ was explained as "a fractional change in volume as a measure of the increase in randomness" (related to $\frac{dQ}{T}$) How does ...
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3answers
406 views

Is the flatness of space a measure of entropy?

This is a bit quirky: For a very long time I've found Stephen Hawking's evaporating small black holes a lot more reasonable and intuitive than large black holes. The main reason is that gravity is ...
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186 views

Gauge fixing the Einstein's gravity action

This is in reference to this paper, arXiv:1204.4061. I was wondering if someone can give me a reference which explains this gravitational gauge fixing that they have done in $2.10$ and how that ...
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123 views

How irreversible processes are possible?

Susskind says that all laws of mechanics are reversible and any valid mechanic law most be reversible: you can always determine the previous state of any physically valid system. However, the simplest ...
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1answer
105 views

In calculating entropy, why can the partitioning of an ensemble into microstates be chosen “somewhat arbitrarily”?

I'm confused by statistical entropy. It seems to me like the number of microstates for a given macrostate would increase without bound as finer partitionings of the phase space are chosen. Why is it ...
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2answers
114 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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1answer
132 views

Explain entropy (again)

I think I understand entropy finally. Will you verify for me? $$S = k_B \ln( \Omega)$$ where $\Omega$ (the multiplicity) is the degeneracy of the system at some energy (E)? So if the system is a ...