# 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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### Is a spontaneous decrease in entropy *impossible* or just extremely unlikely?

I was reading this article from Ethan Siegel and I got some doubts about a sentence about entropy, specifically when Ethan explains the irreversibility of the conditions of the hot-and-cold room, as ...
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### Why is Maxwell's demon taken seriously as a challenge to the second law of thermodynamics?

Supposedly, Maxwell's demon, a thought experiment, is a challenge to second law of thermodynamics, an experimental law. Relativity started in the same manner as a thought experiment, but the obvious ...
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### Should the same amount of heat increase entropy less in larger systems?

Suppose I have some simple isolated system, so the entropy is given (according to the Wikipedia page on Hemholtz free energy) by $$S = k\log Z +\frac{U}{T}+c$$ where $Z$ is the partition function, $U$...
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### Entropy change in sudden expansion

For an irreversible sudden expansion from $V$ to $2V$, no heat is added during the expansion. However, the entropy changes by $N\log2$. I'm not sure how there can be a change in entropy without any ...
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### Can we prove Liouville's theorem from Noether's theorem?

We can prove that gibbs entropy is preserved from Liouville's theorem. We can also prove that its conserved from Noether's theorem and the time reversal symmetry of the Hamiltonian. But it seems ...
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### Is it possible to derive the canonical ensemble without the microcanonical one?

I'm trying to understand if the microcanonical entropy $S_{mc}=\log(\Omega)$ with $\Omega=\int\frac{d\vec{z}}{h^{3N}N!}\theta(E-H(\vec{z}))$ is somewhat more "fundamental" than the canonical ...
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### Entropy of photons in the Sun / Earth system - Do infrared photons have higher entropy than ultraviolet/visible photons?

The entropy of a photon gas in equilibrium (emitting e.g., black-body radiation; BB) is $S \propto V \cdot T^3$ where $V$ is the volume and $T$ is the temperature of the gas [see https://en.wikipedia....
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### What exactly is entropy?

How is $\frac{dQ}{T}$ measure of randomness of system? What is entropy really? The answers to these questions sum up the thermodynamic meaning of entropy. But, I have seen way too many documantaries ...
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### Holographic Entanglement Entropy for a mathematician

I'm not sure if this is an appropriate question for this site, but figured I'd give it a shot. I'm a mathematician (with an extremely limited background in physics) and have come across some ideas ...
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### Do people work on improving battery efficiency by increasing entropy difference?

I have been reading a Daniel Schroeder's book called "An introduction to Thermal physics", and after having completed first couple of paragraphs of "Free energy as available work" (...
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### Temperature dependent heat capacity and entropy

this problem is often presented as a simple demonstration of relationship between the heat capacity at constant volume $C_V$ and entropy $S$. Let's say the heat capacity $C_V$ is equal to $a T + b T^3$...
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### Are Black Holes high and low entropy?

Some time ago I read that without knowing more about quantum gravity the assumption that Black Holes continue to collapse is valid. That mystifies me somewhat but for the purpose of this question I’m ...
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### What are the relevant macroscopic variables for a 'bitgas'?

The classic macroscopic variables one typically measures for an ideal gas are $P$, $V$, $T$, $n$, - pressure, volume, temperature, and amount, respectively. I am curious what the corresponding ...
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### What is an example of a system with non-vanishing topological entanglement entropy at finite temperatures?

In this paper: https://doi.org/10.1088/1367-2630/14/3/033044 it is show that for Kitaev toric code looses topological entanglement entropy over long times if it is thermally opened. What is an example ...
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### Does a book get lighter if you rearrange the letters?

I'm wondering if the information lost by rearranging the letters of a book is measurable as a difference in its initial and final mass. Choose a long, random string over an alphabet, say $\{0,1\}$, of ...
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### If the existance of life is a mechanism of nature to maximize entropy, then why haven't humans nuked the current entropy up? [closed]

Just remembered hearing that the existence of life doesn't contradict the assumption about entropy (the 2nd law of thermodynamics.) If so, why is the overall entropy only increasing at such a slow ...
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### Thermodynamics of RN black holes [duplicate]

The RN metric in asymptotically flat spacetime is given here: Wikipedia page on RN metric. From the metric, we can work out the Bekenstein-Hawking entropy to be S = Area/4 , which explicitly would be:...
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### How do scientists produce entangled photons?

In many experiments like the Delayed Choice Quantum Eraser Experiment, scientists use entangled photons. How do scientists make/obtain them? What is the realistic level of control scientists have ...
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### Multiplication of phase spaces for entropy

I have a problem understanding the phase space volume of entropy in the following example: To make it easy let's say we have a system with one dimension, two particles & and a rough discretisation ...
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### Is entropy maximum in equilibrium?

Usually, in the context of non-equilibrium thermodynamics, it is said that entropy achieves a maximum in equilibrium, so the Taylor series expansion of entropy around the equilibrium state as a ...
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### Why does minimization of free energy result into an almost uniform distribution of protein foldings?

I have just found out that proteins (at least in some cases) are folded into their functional conformation (i.e. their functional folding), through thermal fluctuations, and that this conformation ...
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### Von Neumann Entropy of $n$ qubits

Why is the maximum entropy of $n$ qubits (in $\log_2$ units) equal to $n$? How does one calculate $\operatorname{Tr}(\rho \operatorname{log} \rho)$ (since $\log \rho$ must be expanded). What is even ...
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### How does entropy increase when measuring something?

If I have a gas that starts in a corner of a box it will have low entropy. I have a detector on the corner that measures "1" if all the particles are at the corner and "0" otherwise. If I let the ...
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### Calculating entropy change in water and copper? [closed]

A student submerges one tip of a copper bar into a reservoir of boiling water at 100 ° C and the other tip in a mixture of water and ice at 0 ° C. Both bars are isolated. After the bar reached a ...
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### Entanglement entropy under a particular transformation

Consider a state $|\psi_0\rangle$. I am acting with an unitary transformation U on this state, due to which this becomes: $$|\psi\rangle = U|\psi_0\rangle$$ I want to see how the entanglement ...
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### Why the reversibility requirement in Clausius equality doesn't prevent defining the entropy from it?

In his original work Clausius defines the entropy from his equality $\oint \frac{\delta Q}{T}=0$, which holds for a reversible cyclic process. As it means the integral $\int \frac{\delta Q}{T}$ over a ...
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### Why are probabilities for each micro-state equal within a micro-canonical-ensemble?

This question is about statistical mechanics: Why does it make sense to postulate, that in thermal equilibrium all micro-states with fixed U within a micro-canonical ensemble are equally probable? ...
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### What is the amount of information carried by a $X$-bit system?

Please consider me a beginner and not an expert by any means. My question below will thus be very very simple as that of an uninitiated. Let me consider four simple physical systems with ${\rm N}_S$ ...