# Questions tagged [entropy]

An 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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### Where is the flaw in this brownian ratchet design?

As I understand, Brownian ratchets do not work because the paddle, which is supposed to keep the gear spinning in a single direction, also oscillates with thermal noise. A the paddle can dissipate the ...
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### Informational content of a single symbol

In the communication context, every book i've started to read says: if you want to send a datum about a random experiment $X$, let it be a fair coin toss, that is $$p(tails)=p=0.5; p(heads)=q=0.5$$ ...
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### Why don't time crystals violate the Second Law?

Why don't time crystals violate the Second Law of thermodynamics and why aren't they "time machines"?
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### Why did people think that black holes have zero entropy before the works of Bekenstein and Hawking?

To the extent I know, before Bekenstein and Hawking, the general consensus among physicists was that the black holes have zero temperature and zero entropy. I can possibly understand why people would ...
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### Entropy as a multiplicative measure of disorder as opposed to an additive one. Probability distribution?

Entropy $S,$ is usually defined as an additive measure because mathematically and physically speaking it's usually easier to work with. I'm wondering how to write entropy as a multiplicative measure......
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### Normalization of the partition function

I am used to think that multiplying the partition function by a constant is meaningless, and shouldn't change any calculation, as under $Z' = A Z = A \sum_n \exp(-\beta E_n)$ for an arbitrary $A$, the ...
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### Is decreasing a system's enthalpy equivalent to increasing the entropy of the universe? [closed]

Consider a ball dropped off a cliff: the system (i.e. the ball) has lowered its energy while the surroundings have increased theirs. Energy is conserved, yet the energy considerations provide no ...
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### A 'better' definition of time [closed]

I have been annoyed by official definitions of time from many Google searches and decided after listening to Sean Carroll's podcast to write my own. Here is what I did so far: What is time? A state ...
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### Does "very non-extensive" quantum matter exist?

This is a two-fold question: I have read that the entropy of a black hole is proportional to its surface area. It left me wondering if it is possible to create some (non-trivial) quantum matter with ...
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### Entropy of perfect gas function of internal energy and number of particles [closed]

In a statistical physics lecture, I found an equation describing the entropy $S$ of an ideal gas and it is said that equation can be obtained thanks to elementary thermodynamics formulae. The equation ...
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### The second law and the advantage of measurement?

Background To the best of my knowledge, almost all living systems make use of information obtained from sensory organs. If this result is a reflection of natural selection, then this fact suggests ...
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### How can free expansion be truly irreversible if particles have a small chance of returning to their original state?

According to Halliday-Resnick, a free expansion of a gas is an irreversible process. However, the text continues that in a system of particles in a box, it is possible (though very unlikely) for a ...
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### Relative entropy and Lagrange multipliers

I'm reading Barnett's 'Quantum Information Theory' and at some point, he uses Lagrange multipliers to show that the relative entropy is nonnegative (everywhere I looked the proof ends up using Jensen'...
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### Possibility of Violating Second Law of Thermodynamics

A common climate change denier argument is that back-radiation proposed by climate-change theory violates the second law of thermodynamics because it implies that a cold body warms a hot body. My ...
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### Making sense of Entropy being energy over temperature

Over the internet, I found many resources that explain very well what entropy represents. However, the dimensions still appear hard for me to make sense of: energy, simply put, is the ability to do ...
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### Will withdrawing electricity via a thermoeletric device cool a whole closed system?

If a hot and a cold container are placed thermo sealed system, and a thermoelectric device is used between them and electricity is withdrawn that way, will the resulting entropic temperature in both ...
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### Entropy after removing partition separating two gases system

An ideal gas is seperated by a piston in such a way that the entropy of one prat is$S_1$ and that of the other part is $S_2$. Given that $S_1>S_2$, if the piston is removed then the total entropy ...
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### Can the universe be considered an isolated system?

Is it allowed to consider the physical universe as a thermodynamic isolated system obeying the general second law since the total entropy in a comoving volume does not decrease with time despite ...
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### How does the statistical definition of entropy reduce to $S=k_b \ln (g)$?

How can we go from the Gibbs form of entropy $$S=-k_\mathrm B \sum\limits_s P(s)\, \ln P(s)$$ to the Boltzmann form $$S=-k_\mathrm B \ln(w)$$ where $w$ is the multiplicity? Is it simply enough to say ...
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### Is the entropy of a black hole relative?

I have a question about the entropy of black holes. Well, some time ago I was able to demonstrate theoretically that the entropy of black holes should be relative, that is, depend on the observer. But ...
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### Is entropy of planets and others bodies proportional to the area?

Is entropy of planets and others bodies proportional to the area? If yes, how do I prove that? I know it works for a black hole but, and for others? If no, then the entropy is really proportional to ...
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### Change of entropy [closed]

An ideal gas is heated in a constant pressure process such that its final temperature is twice the initial temperature, the corresponding entropy change in ideal gas is $\Delta S$. If the same mass ...
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### Definition of entropy for relativistic fluids

In section 5.2 of (https://link.springer.com/article/10.12942/lrr-2007-1) ( version on Arxiv ), the authors mention that the equation of state $\rho=\rho(n)$ for a single relativistic fluid system can ...
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### Relation between reversible and irreversible nature of engine and its entropy [closed]

please someone tell me about the relationship of the reversible and irreversible nature of an engine and how is it related to its change in entropy
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### Understanding Daniel Schroeder's comic of interpreting enthalpy and Gibb's free energy

In this answer by Steeven on the meaning of Enthalpy, the following image is used to explain it: In this comic, I don't understand two things: Why is the energy required to make space for the rabbit ...
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### Entropy of micro canonical ensemble [closed]

Entropy of rolling a dice assuming to be a micro canonical ensemble is given by : I know $S = K \space ln \space\Omega$ but how to find $\Omega$ ( No. of ways in which dice can arrange itself ) ?
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### Dependence of entropy on topology?

In black hole thermodynamics, there is a nontrivial dependence of thermodynamical entropy on the area of the event horizon which is a geometric object. I want to know how this may be intuitively ...
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### "Increase in Entropy Principle"

I have a question about the "Increase in Entropy Principle". As you can see from the figure, For adiabtic processes $\Delta S>0$. This is because of the Eq. (3). If I consider the ...
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### Local decrease of entropy, does it require life?

Universal entropy can decrease only locally at the expense of bigger increase elsewhere. Can this occur in a lifeless environment or does it necessarily require living organisms to do it? Can this ...
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### Why doesn't an ideal gas undergoing an isobaric process violate the second law of thermodynamics

I have been stuck on this for the past few hours, and still have got no resolution: Let's say that we have an isobaric process being done by $1$ mol of a gas. Accordingly, we'll be using gas laws and ...
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### Quantitative relation between entropy and time

Increase in entropy gives us the arrow of time. But is there any quantitative relation between these two quantities that relates the entropy change with time interval? Any literature/text/paper on ...
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### Does entropy change when work in done on the system?

Suppose, I have a cylinder filled with ideal gas molecules, and a piston is fitted at the top of the cylinder so that work can be done on and by the system. Now, if I do work on the system, isn't it ...
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### What is meant by the localization of a wave function?

Shannon entropy, in terms of position space wave functions, can be written as, \begin{equation} S= -\int^{\infty}_{-\infty} \vert \psi(x) \vert^2 \log \vert \psi(x) \vert^2 dx. \end{equation} In ...
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### How to compute entropies from a lattice model in a dissolution problem

I'm currently working on problem set 3 from the MIT OCW 20.011J course on Statistical Thermodynamics for Biology/Chemistry (link) I'm stuck starting from parts b onwards. I've taken multiple attempts ...