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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Integrating entropy on an arbitrary boundary [migrated]

Entropy, denoted as H, is: $$ H = -\int_a^b p\ln(p) dx $$ where the range a to b is some arbitrary boundary and where p is given by the classic: $$ p(x) = ...
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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 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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42 views

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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25 views

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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49 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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36 views

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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159 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.thus require ...
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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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35 views

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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36 views

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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3answers
97 views

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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28 views

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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192 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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1answer
52 views

(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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61 views

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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41 views

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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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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610 views

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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63 views

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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Callen Thermodynamics 2.8-2 help? [closed]

A two component gaseous system has a fundamental equation of the form $S=AU^{1/3} V^{1/3} N^{1/3} + \frac{BN_1N_2}{N}$ where $N=N_1+N_2$ and $A$ and $B$ are positive constants. A closed cylinder 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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1answer
146 views

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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69 views

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
29 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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43 views

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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121 views

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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71 views

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} ...
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Is there a thermodynamic limit on how efficiently you can solve a Rubik's cube?

Suppose I build a machine which will be given Rubik's cubes that have been scrambled to one of the $\sim 2^{65}$ possible positions of the cube, chosen uniformly at random. Is it possible for the ...
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1answer
62 views

Prove that $-\log{d} \leq H(A|B) \leq \log{d}$ for von Neumann entropy

I'm trying to prove that $-\log{d} \leq H(A|B) \leq \log{d}$ for von Neumann entropy. Now, for this to make sense I should give some definitions. System $A$ lives in Hilbert space ...
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Is the equilibrium state in thermodynamics a consequence of the second law of thermodynamics?

Is the thermal equilibrium state the state of maximum entropy? Is it a consequence of the second law of thermodynamics?
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Behavior of maximum entropy states in a closed system?

As I understand it, entropy is a measure of the number of permutations of microstates of a system possible, without changing the observed 'macrostate variables' / measurements or properties of a ...
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51 views

How does the universe store information

I have read that entropy is responsible for the storage of information in the universe; that information increases with entropy increase. and that information is never lost. Is this correct? But ...
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70 views

Ideal chain / entropic spring - what is the *microscopic* force?

The ideal chain is the classic example of an entropic force. Usually one derives this force from the fundamental relation describing forces in the canonical ensemble: $$ \tag 1 F = (\partial \langle E ...
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Does Noether's theorem apply to entropy?

Entropy appears to have a translation symmetry - adding some constant value to it doesn't appear to my fairly rudimentary understanding of physics alter the actual physics. Is this correct? Now ...
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Is entropy absolute (as in absolute temperature)?

Following this question on the Entropy at the Big Bang where I asked: Since Entropy always increases (in general); its expected that the entropy at the beginning of the universe should be the ...
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1answer
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Definition of Entropy for reversible and irreversible process

$\int \dfrac{\delta Q}{T}$ can't be used to calculate entropy of an irreversible process. If you happen to know heat supplied and temperature at which it is supplied for just an instant. Can you then ...
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Entropy of loops in the PV plane

The change in entropy of the Carnot and reversible cycles is said to be 0. Several other loops are supposed to have a non-negative change in entropy. This presents 2 problems which I cannot ...
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Is Boltzmann distribution contradicting with the fundamental assumption of statistical thermodynamics?

In equilibrium statistical physics the fundamental assumption of statistical thermodynamics states that the occupation of any microstate is equally probable (i.e. $p_i=1/\Omega, S=-k_B\sum p_i\,{\rm ...
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292 views

Entropy of the whole universe

In "Thermal Physics", Charles Kittel proves that entropy always increases in systems when the degree of freedom are increased (adding particles, adding energy, expanding volume, etc ). I started to ...