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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1answer
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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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Examples of processes that are reversible isentropic but not adiabatic?

Since $ds=\frac{dq_{rev}}{T}$ for reversible processes it seems we can have reversible isentropic processes that are not adiabatic provided the temperature changes in such way that the sum of $\frac{...
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What microscopic and microscopic parameters are involved if room is filled with normal air?

Let us suppose that in my room an air conditioner is working at $25^\circ\ C$. Now if I want to calculate the macroscopic and microscopic coordinates in the room if it's completely filled with normal ...
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Mathematical proof of Maxwell's Demon

I am learning thermodynamics, and came across the interesting topic of Maxwell's demon, which says, that you can decrease the entropy of a system. However, I am trying to see this mathematically. The ...
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1answer
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Reversing entropy by statistics

If the second law of thermodynamics is about statistics, there's a chance of a specific microstate of a very unlikely macrostate happen, so the entropy would be reversed. So, the Universe could return ...
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1answer
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Is there a non-information theoretic justification of the maximization principle of entropy?

All modern derivations of statistical quantum mechanics I've found in the literature, have relied on the axiom, that the physical density operator is the one which maximizes the Von-Neumann entropy $$ ...
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1answer
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Compression in a heat pump with dissipation loss

I'm reading an introduction into heat pump cycles right now, and have question about the compression part: The optimum compression would be an adiabatic one, after which you end at a certain ...
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Why don't the gas molecules accumulate at one corner of an isolated box?

If for an isolated system in thermodynamic equilibrium all the accessible microstates are equally probable, why do the gas molecules in an isolated container, never accumulate at one corner of the box ...
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Hoe does the entropy in BCS superconductor behave?

In low-temperature superconductor the formation of Cooper pairs results with zero resistinvity. The transition to the normal state is second-order phase transition. In Ehrenfest classification it ...
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Does writing a file to a solid state drive change the mass? [duplicate]

Some stupid meme my sister showed me went along the lines of "will my laptop get heavier if I put more files in it?", but it was sufficient to get me thinking--is there an energy change &...
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Why can a system energy defined by entropy? [closed]

Energy define as (wiki page minimum energy of system in last section) $E=ST -PV+\mu N$ $P$ is pressure and $V$ is volume, $Ν$ is the number of particles in the gas. Entropy $S$ measure as the log of ...
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Lose cosmological entropy in conformal cyclic cosmology?

In PBS Space Time "What Happens After the Universe Ends?", it is stated that black holes are needed to destroy entropy before a new aeon can start in a low-entropy configuration, which seems ...
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Could a solid body have arbitrarily low entropy but arbitrarily high temperature?

Could a solid, isolated body have arbitrarily low entropy but arbitrarily high temperature? I'm trying to build an intuition: if according to statistical mechanics, entropy is a measure of disorder ...
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1answer
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Is this the Sackur-Tetrode equation or some other equation for entropy?

In my thermodynamic's course, this equation was presented as the Sackur-Tetrode equation: $$\frac{S}{n}=R\log{\left(\frac{V/n}{V_{0}/n_{0}}\right)} +c_v^{*}\log{\left(\frac{T}{T_0}\right)} + \frac{S_0}...
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The simplest possible thermodynamic identity of a solid crystal, including a varying entropy and number of oscillators

I would like to know if the term: $PdV$, can/should be included in the thermodynamic identity of a solid crystal. Let me clarify that the specific crystal is supposed to be having lost, a small $(\...
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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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2answers
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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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1answer
51 views

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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Integrating factor

How can I show that if N is an integrating factor also the product f(S)N is an integrating factor? With S the entropy defined as $$ dS = \frac{dU+pdV}{N}$$ Here's my attempt $$ \frac{dU+pdV}{N f(s)} ...
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Does the number of accessible microstates decrease overall when heat is transferred?

We have two systems of ideal gas with different temperatures. $N$ & $V$ are being kept constant. The number of accessible microstates of each gas is thereby only influenced by a change in $E$. ...
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1answer
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Will entropy continue to increase in an accelerating-expanding universe?

Before/at/during the Big Bang, quantum fluctuations progressed until there was a constant energy density somewhere which caused inflation. The slight variations in energy due to those quantum ...
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What does the plot of the universe's Entropy versus Time starting from the big bang look like?

What does the plot of the entire universe's Entropy versus Time starting from the big bang look like? Is it even possible to create such a figure?
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Do organism produce more entropy as they get more complex i.e. does biological evolution mean decrease in efficency? [closed]

Consider a cell. It has more efficiency than a human being even though a human being is a bulk of cells: The cell has fewer losses when it converts the food it ate for nutrition to do some sort of ...
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1answer
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Infinities in the diagonal matrix while calculating Von Neumann entropy

Consider the example case:$$|\phi\rangle=\frac{1}{\sqrt{2}}(|01\rangle-i|10\rangle)$$ From this we can easily calculate the density matrix:$$\rho=\frac{1}{2}\begin{bmatrix}0&0&0&0\\0&1&...
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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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1answer
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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 ${\rm N}_S$ ...
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How does the philosophy of 'Emergent Gravity' differ from that of 'Quantum Gravity'?

How are the two approaches of understanding gravity, the so-called 'Emergent/entropic gravity' and 'Quantum gravity' (String theory, LQG etc) differ from each other? I am very curious and will ...
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Obtaining the direction of flow from principle of increase of entropy?

Can we mathematically show that water flows from high-pressure region to low-temperature region and why particles flow from a region of higher chemical potential to lower on the basis of the principle ...

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