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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Does entropy apply to Newton's First Law or does “acted upon” always require an external factor?

First law: Every body remains in a state of rest or uniform motion (constant velocity) unless it is acted upon by an external unbalanced force. This means that in the absence of a non-zero net force, ...
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Are information conservation and energy conservation related?

as evident from the title, are both, conservation of energy and conservation of information two sides of the same coin?? Is there something more to the hypothesis of hawking's radiation other than ...
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Are reversible adiabatic processes always isentropic?

If my understanding is correct, neither reversible nor adiabatic processes are necessarily isentropic. But are reversible adiabatic processes always isentropic?
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Nonextensive statistical mechanics

I know that the Tsallis($S_q$) entropy is called nonextensive information measure in the sense that if $P$ and $Q$ are two probability distributions then $S_q(P\times Q)=S_q(P)+S_q(Q)+(1-q)S_q(P)S_q(Q)...
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What is the cause for the inclusion of 'thermal equilibrium' in the statement of Ergodic hypothesis?

This is the fundamental assumption of statistical mechanics: In an isolated system in thermal equilibrium $^1$, all accessible microstates are equally probable. But why does it mention the ...
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Quantum entropy in term of density matrix

Why in von Neumann expression of quantum entropy we have trace of density matrix expression? Why don't off diagonal term play a role?
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Deriving the Boltzmann distribution using the information entropy

I was going through my lecture notes and I found something I could not quite understand. First, it starts by deriving an expression for the information entropy (as used in physics?): Let $p_i$ be the ...
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Relation between Casimir and hydrophobic effects

Background Some years ago I was studying "Fundamentos de biología" (Biology fundamentals) and learned how the lipids create a bilayer due to the water repulsion. Some time later I learned that this ...
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Extracting work from a partition of equally energetic “colored” balls

I am referencing this answer by Ruben Verresen to this question: Does entropy depend on the observer? A bit down in that answer Ruben states that just being able to perceive (in theory - in your ...
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Second Law of Thermodynamics and heating a blackbody with another blackbody

Given a large blackbody with surface area $A_1$ and temperature $T_1$, let's assume I can use some mirror and lens system to capture all the emitted radiation and transfer this energy to a smaller ...
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Can indistinguishable microstates evolve into different macroscopic states?

I guess this question is more about definition than about any physical principle. Can a given physical system (or can there be a physical system) admit microstates that have identical macroscopic ...
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What are the arguments towards the Life-and-Entropy relation?

I've heard it from a few people, and I've seen it popup here in the site a couple of times. There seems to be speculation (and studies?) towards this idea, and this is what I've picked up so far: ...
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The definition of entropy in quantum mechanics

I have seen entropy with several different definitions. Like Von Neumann entropy and Rényi entropy, etc. So I am curious why there are so many different definitions in quantum mechanics while only ...
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Does Entropy Change Depend on the Process?

The entropy is a state variable, so the entropy change should not dependent on the path between the initial and final state. That's why we can calculate the entropy change of free expansion with an ...
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Entropy before and after collapse of the wavefunction and interpretation?

Seems like it might be pretty rudimentary but I want to see if my thinking is on the right track as well as what the result means. The question is, is the entropy of the collapse of a wavefunction or ...
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Entropy definition, additivity, laws in different ensembles

I started studying Statistical Mechanics and specifically - microcanonical ensemble, which consists of defining different quantities such as temperature and entropy, and deriving some thermodynamic ...
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Is quantum entanglement “observer dependent”?

See also here. According to the answers of the mainstream entanglement should be objective. Once more this question asked in a more mathematical way... Any vector $|{\psi}>$ of norm 1 in a Hilbert ...
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Why are $S = -k_B\sum_i P_i \ln P_i$ and $S = k_B \ln\Omega$ equivalent?

This might be a silly question, but I don't see the equivalence relation between these two equations. Could somebody explain to me how to derive one from the other? Thanks in advance!
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About parametrizing quadratic fluctuations in the metric about $AdS_2 \times S^2$

I am referring to the contents of page 20-23 of the paper, http://arxiv.org/abs/1108.3842.pdf Equation 4.5 seems to suggest that one wants to restrict the metric fluctuations $h$ to a subset such ...
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Is there really such a thing as an irreversible process?

If an isolated system goes from a state A to B, will it always eventually fluctuate back to state A? If not, give an simple example. Is it right to say that entropy only says that the probability ...
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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) affected?
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Do gravitational waves have entropy?

We know, according the current understanding of black holes and General Relativity, as well as quantum fields in General Relativity, that black holes have an entropy proportional to the area of the ...
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Second law of thermodynamics and the arrow of time: why isn't time considered fundamental?

I've come across this explanation that the "arrow of time" is a consequence of the second law of thermodynamics, which says that the entropy of an isolated system is always increasing. The argument is ...
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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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While holding an object, no work done but costs energy (in response to a similar question)

I read the answer to Why does holding something up cost energy while no work is being done? and wanting to know more, I asked my teacher about it without telling him what I read here. Instead of ...
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Entropy as a state property

The usual "proof" entropy is a state property is like that: "Consider a system which undergoes a reversible process from state 1 to state 2 along path A, and let cycle be completed along path B, ...
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Does evaporation decrease entropy?

I have a container of water in thermal equilibrium (there are no temperature fluctuations inside the container). Some molecules will evaporate out of the container of water thus decreasing its ...
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Second law of Thermodynamics: Why is it only “almost” always true that entropy is non-decreasing? [duplicate]

Wikipedia - Second law of thermodynamics: ...the entropy of any closed system not in thermal equilibrium almost always increases. I understand that the second law of thermodynamics is based on ...
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Intuitively, why does removing solutes cost $k_B T$ of free energy per molecule?

I can calculate that if you want to, for example, desalinate water, you will have to pay a free energy cost of $k_B T$ for each ion you remove. In other words, removing an ion from a volume of water ...
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Second law of thermodynamics and a bunch of magnets

Say I put a bunch of powerful square magnets on a nearly frictionless table in a disordered fashion. The second law of thermodynamics states that the system shall spontaneously get more disordered, ...
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What causes a eutectic point?

What causes the melting point depression known as a eutectic point? The temperature depression of a eutectic point can be calculated from the enthaplies and entropies of fusion of the two substances....
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Entropy of two expanding and mixing ideal gases

I am currently stuck with the following problem: ...
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Second Law of Thermodynamics…confusion over an example

By the second law of thermodynamics, you shouldn't be able to use any amount of mirrors/lenses to focus sunlight onto an object and heat it past the surface temperature of the sun (approximately 5800K)...
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How does the statistical definition of entropy reduce to heat engine entropy?

In statistical mechanics, entropy is defined in terms of the probability distribution of the microstates of the system, by the Gibbs formula, $S = -k_B\sum_i P_i \ln P_i$. How does that reduce to $dS =...
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If particles can find themselves spontaneously arranged, isn't entropy actually decreasing? [duplicate]

Take a box of gas particles. At $t = 0$, the distribution of particles is homogeneous. There is a small probability that at $t = 1$, all particles go to the left side of the box. In this case, entropy ...
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Does entropy really always increase (or stay the same)? [duplicate]

Consider this image. If the big (grey) molecules were all to spontaneously move to the left, and the small ones were to move to the right, there would be an increase in order. While unlikely, wouldn'...
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Wasn't the Hawking Paradox solved by Einstein?

I just watched a BBC Horizon episode where they talked about the Hawking Paradox. They mentioned a controversy about information being lost but I couldn't get my head around this. Black hole ...
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Do information entropy and thermodynamic entropy evolve the same way?

Recently I asked a question about the relationship between Von Neumann entropy and heat transfer. The link is here. Is the Von Neumann entropy related to heat transfer? I feel as though the answer ...
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When is entanglement entropy the same as free energy?

I am given the feeling that there exists scenarios when this equality holds. Can anyone state/refer to the situations? One case that I hear of is that for $2+1$ CFTs the entanglement entropy across ...
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Entropy of de-Sitter spacetime and the $10^{120}$ vacuum discrepency

While doing some lazy calculations, I came across a curiosity that I'm unable to interpret. It is well known that the cosmological constant $\Lambda \sim 10^{-52}~\mathrm{m^{-2}}$ is usually ...
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Potential energy in stretched vs unstretched rubber bands

I have been searching for a definitive answer to this question but I have been unable to find it. I understand that when you stretch a rubber band, it gives off heat - an exothermic process - but at ...
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von Neumann Entropy of a joint state

Definition 1 The von Neumann entropy of a density matrix is given by $$S(\rho) := - \mathrm{Tr}[\rho \ln \rho] = H[\lambda (\rho)] $$ where $H[\lambda (\rho)] $ is the Shannon entropy of the set of ...
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Entropy: subjective lack of knowledge that leads to objective conclusions

There is something I really don't get about entropy. Let's consider a classical system (not quantum mechanics here). We can compute the entropy of a system via the formula $$S=-\sum_l P_l Log(P_l)$$ ...
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What was the informational content of the universe at the Planck time?

If the energy of $1 \, \mathrm{bit}$ of information is $k_{\small{\text{B}}}T \ln{2}$, then the energy of that bit increases with the temperature of the system. When I try to calculate how much energy ...
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An equation for chemical potential from the Boltzmann entropy equation

I am trying to derive an equation for chemical potential from Boltzmann entropy and this is what I have come up with so far: $$S = k\ln{\left(\frac{N!}{N_\mathrm{up}!\,N_\mathrm{down}!}\right)} \...
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Is the Von Neumann entropy related to heat transfer?

The Von Neumann entropy of a QM system, as far as I understand it, is a measure of the information a particular observer has about that system. Is this definition of entropy directly related to heat ...
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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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Thermodynamics second law variational statement query

In thermodynamics as I understand entropy is a state function. A state function is a property whose value does not depend on the path taken to reach that specific value. In contrast, functions that ...
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Is it true that only living things and man-made objects can make an endothermic process that decreases entropy?

I'm not trying to apply the 2LOT to only part of a system. I'm asking if there is a related law or kind of a sub-law. My highschool physics teacher said that if I take an ice cube and shine a bright ...
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How is the efficiency of a heat engine related to the entropy produced during the process?

I'm reading Schroeder's An Introduction to Thermal Physics. Regarding heat engines, it is stated: Unfortunately, only part of the energy absorbed as heat can be converted to work by a heat engine. ...

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