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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Why is Entropy's Definition Useful?

I have somewhat of an understanding for other physical quantities, but as far as entropy goes I only know it to be "disorder". Why is the change in entropy formula an appropriate/useful definition, ...
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Confusion on entropy in the universe [closed]

I was researching about the heat-death of the universe, and I was wondering if my understanding of it so far is factual to the theory? However, the 3rd Law of Thermodynamics prevents the universe’s ...
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Mathematical proof of the Second Law of Thermodynamics

Is there some book or paper that formalizes statistical mechanics, like some people have done with relativity, and proves the second law of thermodynamics from more foundational axioms?
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Why doesn't the entropy of an isolated system of ideal gas change during isothermal compression/expansion?

Even if the system is isolated and there is no heat exchange with surroundings, shouldn't the decrease/increase of pressure result in increase/decrease of entropy ??? Does this property of an ...
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Problems with units of entropy in statistical thermodynamics

The statistical thermodynamics definition of entropy: $S = kN \ln (W)$ troubles me a lot with the problem of dimenstions. where $S$ is entropy; $k$, the Boltzmann constant; $N$ the number of particles ...
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Existence of negative temperatures and the definition of entropy

How negative temperatures can be possible has been treated on StackExchange before (several times in fact), but in light of some recent academic discussion, most of these answers seem to be possibly ...
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Problem about entropy

Combining the first and second law of thermodynamics we can get the following equation $$TdS=dU-P_{ext}dV$$ First question: Is this equation applicable for irreversible processes such that that ...
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Relativity of simultaneity and the second law of thermodynamics? [closed]

Has the connection been noted between these two? I have been studying special relativity and in learning Minkowski diagrams I have noticed that as v approaches c, the relativity of simultaneity is so ...
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Is entropy in quantum mechanics emergent or fundamental?

Since a quantum mechanical system, even an isolated system containing one particle, can be described by a density matrix, with entropy for the system given by $\langle S\rangle=-k \rho\ln(\rho)$, is ...
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Why do we remember the past but not the future?

The question is sometimes referred to as the "psychological arrow of time" (Hawking, 1985). Here the past is understood as a moment or time when the entropy of the universe was lower, and contrarily ...
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Is there a general H-theorem?

In statistical mechanics, Boltzmann showed that for dilute gases the H-function increases. I remember from a lecture that there is no general H-theorem, e.g. for non-dilute gases or in the quantum ...
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Entropy as a state property

The usual "proof" entropy is a state property is like that: "Consider a system which undergoes a reversible process from state 1 to state 2 along path A, and let cycle be completed along path B, ...
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What does the Higgs boson have to do with the uncertainty principle and quantum oscillations?

I was looking in New Scientist the other day when I saw something to do with the Higgs boson, energy levels, entropy, space/time, quantum oscillations and many other things. It was in a feature to do ...
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Entropy of photons

Do low energy photons have greater entropy than high energy photons, or is the entropy of all photons the same (and the relationship between high and low entropy radiation is just a function of the ...
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Do individual photons increase entropy as they travel?

If I draw a control volume around a single light wave traveling through empty space, is entropy increasing as it goes? How is the degradation of the quality of energy manifested?
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Question on entropy

All of my textbooks mention, that entropy-change of all spontaneous physical, and chemical processes is positive, and that such processes need another condition to fulfill- decrease in the net ...
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Why can the entropy of an isolated system increase?

From the second law of thermodynamics: The second law of thermodynamics states that the entropy of an isolated system never decreases, because isolated systems always evolve toward ...
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At an instant, does a system of gravitational charges exhibit equivalent behavior to a time-reversed system of like electric charges?

Question: In principle, does a system of gravitational charges exhibit equivalent behavior to a time-reversed system of like electric charges? (At a single instance in time?) Additional Notes: I am ...
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Proving that Measurement increases von Neumann entropy

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 ...
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Thermodynamics of binary symmetric channels

I am reading this very interesting paper: http://m.iopscience.iop.org/1751-8121/41/40/402002/pdf/1751-8121_41_40_402002.pdf about thermodynamics of channels in information theory. More generally, ...
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About parametrizing quadratic fluctuations in the metric about $AdS_2 \times S^2$

I am referring to the contents of page 20-23 of the paper, http://arxiv.org/abs/1108.3842.pdf Equation 4.5 seems to suggest that one wants to restrict the metric fluctuations $h$ to a subset such ...
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How does the evolution of a solar system not break the second law of thermodynamics?

Please forgive: I am a layman when it comes to physics and cosmology, and have tried finding an answer to this that I can understand, with no luck. As I understand it, the solar system evolved from a ...
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How to calculate the Wald functional?

I want to calculate the Wald functional for arbitrary higher curvature Lagrangians - like getting equation 6.31 from 6.30 in this paper. A priori the above looks like an extremely complicated ...
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Will the black hole size increase?

I was thinking about the following thought experiment, but wasn't sure about its outcome. Suppose there is a black-hole and I enter it with a partitioned box containing two different gases on either ...
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Entropy is constant. How to express this equation in terms of pressure and density?

In hydrodynamics of an ideal, non-compressive flow we use 5 variables: pressure $p$, density $\rho$ and velocity field $\mathbf{v}$. So we need 5 equations. Landau's "Hydrodynamics" states that the ...
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44 views

Entropy / Structure Relations

I want to check on the validity of the following objective definition of order. Is it correct? Is there a more rigorous statement of this concept? The further a system is from its maximum ...
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85 views

Explicit form of the entropy production in hydrodynamics

I'm trying to understand how hydrodynamics arise from a precise, mathematical formulation of thermodynamics, learning mostly from Landau's "Hydrodynamics". So Landau starts from formulating the ...
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Is there a relation between (non-) existence of magnetic monopoles and thermodynamics?

This question follows on previous work on connections between (other) areas of physics and thermodynamics as in here, here and even here. P. Dirac (an electrical engineer initially) was one of the ...
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Is quantum uncertainty principle related to thermodynamics?

Would like to ask a question, but first i would like to say Hello Everybody in a way that plays the system, since some geniouses decided that one should not be able to say hello in a question. The ...
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Does causality alone resolve the mathematical ambiguity of expressing physical systems?

Newton's 2nd law of motion is most often written in the differential form $\sum F = {dp \over dt} $ but can also be expressed in an integral form $ p = \int\sum F dt $ Each form of expressing ...
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51 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 biparte system $AB$, described ...
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Has any possible non-extensive entropy been classified?

How many non-extensive entropies do exist? Tsallis, Havrda-Chavrat, Renyi, Kaniadakis, Sharma-Mittal,... To be more precise, I am wondering if some classification like those of "finite" or Lie groups ...
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entropy in Information theory vs thermodynamic?

We Now From Information Theory That Entropy Of Functions Of A Random Variable $X$ Is Less Than Or Equal To The Entropy Of $X$. Does It Break The Second Law Of Thermodynamic?
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Principle of Caratheodory and The Second Law of Thermodynamics

Background Constantin Carathéodory formulated thermodynamics on a purely mathematical axiomatic foundation. His statement of the second law is known as the Principle of Carathéodory, which may be ...
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Quantum entropy in term of density matrix

Why in von Neumann expression of quantum entropy we have trace of density matrix expression? Why don't off diagonal term play a role?
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The entropy of the universe in an irreversible cycle [closed]

Suppose we have an ideal gas performing an irreversible cycle composed by: an isothermal transformation at $T_{1}$; an isobaric transformation at $P_{A}$; an isothermal transformation at $T_{2}$; an ...
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How can the microstates be measured with zero energy expenditure?

James P. Sethna. Statistical Mechanics. Exercise 5.2: What prevents a Maxwellian demon from using an atom in an unknown state to extract work? The demon must first measure which side of the ...
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Entropy and chemical potential of an ideal gas

I am reading Schroeder's book "Thermal Physics". One calculation in the text was not quite clear to me. The entropy of an ideal gas is given by the Sackur-Tetrode equation: $$ ...
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Classical and Semi-classical treatments of the ideal gas

In the semi-classical treatment of the ideal gas, we write the partition function for the system as $$Z = \frac{Z(1)^N}{N!}$$ where $Z(1)$ is the single particle partition function and $N$ is the ...
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Intuitively, why does removing solutes cost $k_B T$ of free energy per molecule?

I can calculate that if you want to, for example, desalinate water, you will have to pay a free energy cost of $k_B T$ for each ion you remove. In other words, removing an ion from a volume of water ...
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Is entropy a dynamical quantity [closed]

I am confused whether Entropy is a dynamical quantity or not. Gibbs entropy, and quantum mechanical Von Neumann entropy.
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Homemade salad dressing separates into layers after it sits for a while. Why doesn't this violate the 2nd law of thermodynamics?

The oil, vinegar and other liquids in homemade salad dressing separate into layers after sitting for a while, making the mixture become more organized as time evolves. Why doesn't this violate the ...
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Definition of Information in Information Theory

I am not sure in which SE site I have to put this question. But since I have learnt Shannon Entropy in the context of Statistical Physics, I am putting this question here. In the case of Shannon ...
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Entropy $dQ=TdS$ and Work $dW = -pdV$ conditions?

What are the conditions in order for the equations: Entropy $dQ = TdS$ and Work $dW = -p dV$ to work? I think for $dQ = T dS$, it must be a reversible process? But for $dW = -p dV$, shouldn't it ...
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Probability of spontaneous Boltzmann brain formation

I was reading through: http://www.scottaaronson.com/papers/giqtm3.pdf But I can't make sense of page 61 discussing Boltzmann brains. Specifically the fact that it says: But the problem is worse. ...
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Can Entropy decrease through genralized measurement

Can entropy of a quantum state decrease through the generalized measurement?
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Where does deleted information go?

I've heard that, in classical and quantum mechanics, the law of conservation of information holds. I always wonder where my deleted files and folders have gone on my computer. It must be somewhere I ...
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Information or Matter or Energy

Which one is the most fundamental of the universe? What it is made of? Physicists are searching for unique and fundamental form. The question is , information is more fundamental than energy ? ...
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Entropy and the uncertainty principle

According to the second law of thermodynamics, the total entropy of the Universe must always increase after any interaction (as I understand). So in the hydrogen atom, the electron has a high ...
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Relationship between dynamical entropy and chaotic noise

I am interested to know if Kolmogorov Sinai Entropy of a system also known as Kolmogorov Complexity in information theory or popularly known as metric entropy increases with increase in dynamical ...