A important property of all systems in thermodynamics and statistical mechanics. Entropy characterizes the degree to which the energy of the system is *not* available to do useful work

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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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Why is adiabatic process isentropic?

I have read that adiabatic process is isentropic because there is no heat exchange in an adiabatic process and thus no change in entropy. But my question is - Even in adiabatic process, work can be ...
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Why aren't we surrounded by Black holes?

The Bekenstein bound is a limit to the amount of entropy a thermodynamical system can have. The bound is given by the following expression: \begin{equation} S \leq \frac{2 \pi k R E}{\hbar c} ...
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Can entropy of Universe be constant?

If I understand entropy correctly, then for example two objects orbiting a centre of mass have lower entropy than when said objects eventually crash into each other and form a new one. So let's say ...
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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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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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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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Entropy before and after collapse of the wavefunction/ and interpretation?

Seems like it might be pretty rudimentary but I want to see if my thinking is on the right track as well as what the result means. The question is, is the entropy of the collapse of a wavefunction or ...
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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 ...
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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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What is the resolution to Gibb's paradox?

This question is essentially a duplicate of Gibbs Paradox - why should the change in entropy be zero?. The question concerns the following situation: I have some gas of identical particles and they ...
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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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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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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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What is happening as our Universe is expanding? Is entropy increasing or decreasing?

Scientists say that entropy of our universe is increasing as it is expanding and our universe is cooling down gradually from the time of it's birth.If something is getting cooler and cooler then how ...
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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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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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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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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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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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Kolmogorov entropy and noise

There are various ways of calculating the Kolmogorov entropy (KE)of dynamical system. According to Pesin's theorum, it is the summation of the lyapunov exponents; frominformation theoretic concet, it ...
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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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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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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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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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Minimizing Availability vs. Maximizing Entropy

What is the conceptual difference between minimizing the availability of a thermodynamic system and maximizing the entropy of a thermodynamic system? I am under the impression that these are the same ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Boltzmann entropy and phase space volume

In Huang's book on Statistical mechanism and Statistical interpretation of Entropy, it is not mentioned that $\Omega$ is the phase space volume, but it is the states of the system. So, how does ...
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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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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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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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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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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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Heuristic argument for forces with respect to entropic force

Here is an argument that I have with regard to entropic forces and how it can be linked to the other forces in nature. Gravitational: This is debated: whether gravity is entropic or not. I am going ...
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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 ...