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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Link between Hawking-Bekenstein Black hole entropy and entanglement entropy

I'm currently doing a project on two sided Ads-Schwarzschild black holes in the context of Ads/CFT. I want to show that the entanglement entropy between the two CFTs corresponds approximately to the ...
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How can a reversible adiabatic expansion not increase entropy?

In the second stage of the Carnot cycle, a gas is thermally insulated and allowed to expand and do work on the piston. I understand the reason people give is that because entropy is $\,dS = \,dQ/T$ ...
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entropy change during irreversible heat loss [duplicate]

When a thermodynamic system gains heat if the heat gain is irreversible then there is a entropy generation along with the entropy transfer..so is there a similar entropy generation associated with ...
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clausious inquality

Take a reservoir which gains a heat Q irreversibly at temp T from a surrounding at temp T0 then the entropy change of reservoir is given by Q/t and that of the surrounding is -Q/T0...How is this ...
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48 views

Transfer of heat through a finite temprature difference

Consider the following derivation There are two reservoirs at temp A & B at temp T1 & T2 .They are connected by a metal rod such that T1 > T2. Q amonut of heat is transfered ...
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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 ...
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How does gravity increase (or, at least, not-decrease) entropy?

I'm a total physics n00b (i.e. I only know the physics as taught in IT grades, and don't remember much of it), and was talking about entropy (initially, not with the physical implications). My friend ...
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80 views

2nd law of thermodynamics - thought experiment

I have designed this simple thought experiment that seems to contradict 2nd law of thermodynamics. Could you please find a mistake in my reasoning? ...
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43 views

Does a closed system with fixed entropy imply an isolated system?

Just first to clarify, my university notation is $$\text{change in entropy} = \text{entropy flow} + \text{internal production of entropy}$$ I am confused with the term fixed entropy. Does that mean ...
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58 views

Second law of thermodynamics (in terms of entropy)

Is the second law of thermodynamics (in terms of entropy) for closed systems or isolated systems? I thought it must be valid for isolated systems, such as the Universe. But the book Fundamentals of ...
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51 views

Derive the Sackur-Tetrode equation

How do you derive the Sackur-Tetrode equation? I know that you must start off with the multiplicity of a mono-atomic ideal gas: ...
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How does my car's remote keep running?

Two years ago, I got a new car. It comes with a wireless remote that provides keyless ignition and can unlock and lock doors at the press of a button. Just recently, I read somewhere (unfortunately ...
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Why the non-analyticity of free energy function implies phase transition? And what's its connection with other 'higher level' free energies?

I have seen 'free energy' arising from several contexts in very different forms, and each contains different amount of information. For example free energy is defined as the logarithm of the ...
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Entropy - Gas Inside A Closed System Reaches Maximum Entropy

Filling a box with a certain amount of gas with a specific total energy and allowing the gas to reach a maximum entropy state, what happens next? Would the gas remain in a maximum entropy state ...
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46 views

Entropy: Disorder or energy dispersal?

The first definition of entropy given by Clausius is I believe this $$S=Q/T$$ It is as I understand a common fact to understand entropy and maybe often teach it as a measure of disorder through the ...
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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 ...
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Does the second law of thermodynamics take into consideration of attractive interactions between particles?

If one searches Google or textbooks on 2nd Law of Thermodnamics, one usually finds a statement that is either equivalent or implies the following. The entropy of the universe always increases. But ...
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Change in entropy of the Universe for charging/discharging a capacitor

I just need to know what exactly happens when charging/discharging a capacitor. Is there any heat transfer between the capacitor and the surroundings? Is there a heat transfer between other parts of ...
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Specific heat ratio range [closed]

I know that the specific heat ratio, $\gamma$, exists in the range $1 <\gamma< 2$, and I am required to demonstrate a proof of this. I have come across the following proof (but I don't really ...
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1answer
53 views

Can Black Holes Maintain Data Entropy When Formed By a Data Storage System?

It's been shown that black holes don't destroy information. There's a little-known scenario in computer science (Specifically AI) where an advanced civilization creates an artificial intelligence that ...
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Entropy $S$ for canonical (NVT) and isobaric (NPT) ensemble

In case of non-isolates system (NVT or NPT ensemble), I learned I can calculate the entropy, $$S=-k_B\sum_jp_j\ln(p_j)$$ where $p_j$=probability at $j$ state. but I saw that the entropy is also ...
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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 ...
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202 views

Do some of the laws of thermodynamics break down in quantum mechanics?

I do not know if this is a stupid question as I am not an expert in thermodynamics and certainly no expert in QM. So, we know that the laws of thermodynamics are laws based on statistics. They ...
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Why did the universe have a low entropy at the big bang?

Sean Carroll, in his book "From Eternity to Here", asks the following question. Why did the universe have a low entropy at the big bang? in John Cramer version of the Wheeler - Feynman absorber ...
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Is it possible to calculate the information content of matter? How?

I know the Bekestein bound is the upper bound for the information content of a region of space, but is it possible to actually calculate that information content (number of bits, not the bits ...
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getting frm micro to macro entropy problem

For an ideal gas entropy forvolume change from micro to macro can be rewritten as: $S=k\ln W$ $\Delta S= S_2-S_1=k\ln W_2-k\ln W_1=k \ln\frac{W_2}{W_1} $ since we are constrained from derivation ...
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What is the gas entropy as a functional of a one-particle distribution function?

There are some discrepancies on how to introduce entropy in classical kinetic theory. In what follows $f(r,p,t)$ is the usual one-particle distribution function of a monatomic gas, normalised to the ...
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What is time, with respect to universe? [closed]

I want to know what is actually time, not like the measurable quantity. But with some scientific terms Someone said that "time is entropy". Is that true? also what makes time unique?
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Black Hole Entropy Calculation

I was watching "Leonard Susskind on The World As Hologram" ( youtube ). At one point he describes the way Bekenstein calculates the entropy of a black hole. Paraphrasing: Take a minimally sized black ...
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Why is the change in entropy for a given energy input dependent on the temperature?

In my thermodinamics class, we saw that $$dS=\frac{dQ}{T}$$ and $$\Delta S=\int_{a}^{b}\frac{dQ}{T}$$ My question is: why for the same energy input $dQ$ the entropy increases more in lower ...
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Setting constants equal to 1 conditions

I have the following expression for the entropy of an ideal gas in a microcanonical ensemble, $$S=Nk_B\ln \left[ \frac{Ve}{N}\left(\frac{4\pi m e E}{3Nh_0^2}\right)\right] $$ Ideally I would like to ...
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226 views

Mass, energy, and entropy.

I have a seemingly simple question about the relation between these three that for some reason doesn't make sense to me. If entropy is the disorder of a system, then a low entropy state is one of ...
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(No need of 2nd law) Adiabatic and isothermal compressibility relation with specific heat

One classical example of thermodynamics is the relation between the Adiabatic and Isothermal Compressibility Relation with the Specific Heats: Compressibilities: ...
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Does a magnetic field decrease or increase entropy?

My question is just the title: Does a magnetic field decrease or increase the entropy of a system? For example if we apply a magnetic filed to a substance, is the entropy decreased or increased?
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Laplace's demon and spontaneous symmetry breaking

One interpretation of Quantum mechanics is the hidden variable theory. This suggests that if we were to have a complete knowledge of the system at one time then the future states of the system are ...
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83 views

Entropy - does Heat Death occur in a closed system

Does heat death occur in a closed system? (Assuming you can theoretically have some sort of "closed system".
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Where does information go if thermodynamic death?

Often read that until Hawking the black holes were introducing a problem with information. Allegedly information should be unable disappear, while this was happening in classic black holes. What ...
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Is it possible to disprove water memory with an entropy argument?

Water memory was a controversial experiment claiming to provide an explanation supporting homeopathy. The results were largely dismissed as being tainted by experimental error. One possible mechanism ...
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Temperature in statistical mechanics and differentiating entropy

In statistical mechanics, the entropy of an isolated system with energy $E$ (with fixed volume $V$ and chemical composition $N$) is defined as $S(E) = k \log \Omega$, where $\Omega$ is the number of ...
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Entropy and the $2^{nd}$ law of thermodynamics

I have just been introduced to the word "entropy" and as it is my understanding that it is a measure of the randomness and chaos of particles in as system. My textbook list the 2nd law of ...
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Is information a form of energy? [closed]

To better describe my question, do the following experiment: Calculate x=12+26+67+71 Now you might have spent some time in getting the answer. You burnt sugar, you used up energy to get the ...
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How does this new theory of a possible infinitely old universe not violate the second law of thermodynamics

I read the following article: http://phys.org/news/2015-02-big-quantum-equation-universe.html And followed it back to this journal reference : http://arxiv.org/abs/1404.3093 It appears to be ...
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Entropy Inequalities

Hey I am reading this paper Entropy Inequalities by Araki and Lieb. I am trying to prove the following lemma: $$S^1+S^2\leq S^{12}+S^{23}$$ using the following lemmas: ...
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What is the interpretatation of individual contributions to the Shannon entropy?

If $X=\{ x_1,x_2,\dots,x_n\}$ are assigned probabilities $p(x_i)$, then the entropy is defined as $\sum_{i=1}^n\ p(x_i)\,\cdot\left(-\log p(x_i)\right).$ One may call $I(x_i)=-\log p(x_i)$ the ...
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Ternary dimensioned density matrix

I am currently reading this paper: Entropy Inequalities by Araki and Lieb (project Euclid link). And I am not able to understand one step: $${\rm Tr}^{123}\left(\rho^{12}\rho^{23}\right)={\rm ...
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1answer
33 views

What can I do with specific entropy and quality on a state (Rankine Cycle)

I've been working some Thermodynamics problems on Power Cycles and I have noticed that if I'm given a specific quality at the exit of the turbine and considering the adiabatic process I will have two ...
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Entanglement entropy vs entropy

I just read that if you have a pure density matrix state on a product space, then a way to define entropy in a subspace is to take the reduced density matrix state and define $S = 1- ...
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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 ...
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Space-Time and Entropic gravity [closed]

Gravity warps space-time, and Gravity can be thought of as Entropy. (Entropic gravity) So, as spacetime expands, how is space-time Entropy (or the inverse of gravity) effected? (If this is a noob ...
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Why does this entropy change formula for heating water blow up at $T_{1}=0$?

My textbook says: Next we consider a more complicated problem: heating m grams of water, from $T_{1}$ to $T_{2}$. The entropy change is $$S_{2}-S_{1}=\int mc_{w} ...