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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 uncertainty and correlations actualy the same thing?

In this paper on page 2 it is said that The entropy $S(\rho_A)$ measures the amount of correlation (classical and/or quantum) between $A$ with the external world. Now this is confusing me a little ...
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Derivation of Proportionality of Phase Space Volume log(Γ)∝N

In the derivation of extensivity of entropy for the micro-canonical ensemble, we assume an ensemble of two systems with the energies $E_1$ and $E_2$. The total energy is given as $E<E_1+E_2<E+\...
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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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How do we quantify this kind of information in Quantum Mechanics?

Let a quantum system be given with Hilbert space $\mathscr{H}$. Suppose it is described by the quantum state $\rho$, i.e., a density matrix. We can define the Von-Neumman entropy as $$S(\rho)=-\...
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Prove Von Neumann entropy is invariant under coordinate transformation

https://en.wikipedia.org/wiki/Von_Neumann_entropy#Properties How to show that von Neumann entropy for $p_k$ with basis $|\psi_i\rangle$ is the same for $p_n$ with basis $|\phi_i\rangle$? That is, to ...
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Phase transitions and Helmholtz vs Gibbs Free Energy

Gibbs phase rule for Gibbs free energy says that phases during a phase transition must be in mechanical, chemical, and thermal equilibrium, e.g. $T_1=T_2$,$G_1=G_2$, and $P_1=P_2$, where the ...
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What additional percentage of the suns energy is being trapped via green house gases?

Every year we release more greenhouse gases which causes the atmosphere to trap more energy and thus warm the planet. What additional percentages of energy are we talking about here? I would assume ...
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Replacing Qh with Ql in Etropy equation in Heat Pump

In the heat pump below, the $T_H$ is not constant. It is assumes that the process is steady and reversible. So when constructing an entropy equation over the CV (the purple-colored area): $$\dot ms_1+\...
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Does Von Neumann entropy fail to account for projective quantum measurements?

I'm trying to understand if this line of reasoning is correct: For a two-state pure quantum system $\left|\psi \right\rangle=\frac{1}{\sqrt{2}} (\left|0 \right\rangle+\left|1 \right\rangle)$, The ...
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Would it be appropriate to say that in presence of Non-Conservative Forces, the Entropy of System Always Increases?

Would it be appropriate to say that in Presence of Non Conservative Forces the Entropy of a system would always increase? Can we relate Non-Conservative Forces and Entropy in some way? I intuitively ...
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Derivation of Helmholtz free energy and associated relation

I am quite new in thermodynamics and I have never touched it so far. But now I have some basic questions that I hope someone can kindly explain them to me. I know the Helmholtz free energy is ...
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Universal Entropy [duplicate]

I’m a first-time poster... Could entropy possibly be the reason the universe is expanding and even why its expansion is accelerating? If space is not surrounded by anything at all, it would seem to ...
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Breaking Stuff and Putting it Back Together

I was wondering if you could put something back together exactly the way it was before. It takes a certain amount of energy to break something, so theoretically could you put it back together exactly ...
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What are enthalpic and entropic forces?

Am I right when thinking of entropic force to be an entropy minimizing mechanism and enthalpic force to be an energy minimizing mechanism (which is basically an entropy maximization mechanism). What'...
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Von Neumann entropy of a quantum state vs Von Neumann entropy of a system

Using the Chuang and Nielsen Quantum Computation and Quantum Information book, for an introductory course in Quantum Information, I stumbled on an ambiguous (at least for me) use of the Von Neumann ...
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$dQ=Tds$ and quasistatic process

See Ján Lalinský's commment on Entropy $dQ=TdS$ and Work $dW = -pdV$ conditions? My question are: Is there a way to prove that $dQ=Tds$ is a quasistatic process? What's the funcitonal description ...
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Computing entropy for two ideal gas systems

I'm trying to show the processes in the following rows are different. So on the left there are $12$ particles in each box with volume $V=V_1$. Both are divided in three imaginary and equal parts with ...
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Hydrodynamics, isocurvature and entropy

I am trying to figure out what happens in the following situation: You have a fluid that consists of many types of particles that can turn into each other via chemical or nuclear reactions such that ...
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Isentropic expansion and heat capacity [closed]

I am currently trying to learn some basics of thermodynamics. I encountered the following equation $$ \frac{p_2}{p_1}=\left(\frac{V_1}{V_2}\right)^\gamma $$ that allows computing the effect of an ...
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What causes a black hole to be hot?

From my limited understanding of physics, it seems that the heat of a black hole is caused by vibrations in quanta of space, where quanta of space can be viewed as the elementary building blocks of a ...
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Information to Energy equations?

Are there are any known formulas or equations that can calculate information from energy or energy from information? One of them, I believe, is the Bekenstein bound which is the maximum information ...
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How could the early Universe have low entropy when it was so compact? [duplicate]

Entropy of a system can be understood as "the number of states that are macroscopically indistinguishable from the state its currently in". (Sean Carroll, "The Big Picture") Given that the early ...
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How is a superconductor maintaining a persistent current a reversible process?

Once an electric current is established, and then the external electric field/voltage is withdrawn, a superconductor maintains the current forever. Such a process neither violates the first law nor ...
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Earth-like Atmosphere Breaks Second Law of Thermodynamics due to Conduction?

Consider a neutral gas around an Earth-like atmosphere with density, pressure and temperature given by $\rho,\ p$ and $T$ respectively. To keep the system a closed system assume that the atmosphere is ...
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How do you calculate the change in entropy for a non quasistatic process

I understand that Entropy is a state function, but the change in entropy does in fact depend on the process from a-->b. I understand the derivation for entropy where $$S_2-S_1=Ncv\ln\frac{T_2}{T_1}+...
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Ideal Work in adiabatic steady state flow processeses

For calculating ideal work: By applying entropy balance on a steady state flow process we get:- delta(S*mass flow rate) - (rate of heat transfer from system)/Tsurr = 0. Thus according to this ...
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How does the Second Law of Thermodynamics place limits on allowable heat transfers?

I'm confused by the following excerpt from my thermo book, which is referring to a heat engine in contact with two reservoirs: According to the first law of thermodynamics, the net work transfer is ...
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Entropy transfer between finite heat capacity systems

Consider two systems $A$ and $B$ in an insulated vessel with constant finite heat capacities $C_A$ and $C_B$, which are initially at different temperatures $T_{A1} \neq T_{B1}$ for the initial state $...
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Entropy generated for a warm bath heating a cold rock

Put a cold rock of heat capacity $C_r$ and temperature $T_{r1}$ into an insulated fluid bath of finite heat capacity $C_b$ (the bath is not a reservoir) and temperature $T_{b1}$. Now let the entire ...
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Reversible compression of a gas - faulty reasoning?

I am trying to figure out where my reasoning falls apart in this thought experiment: To determine if a process "A" is reversible (or at the very least internally reversible), I try to picture a ...
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Why is the formula for blackhole entropy different that the formula for entropy given by Boltzmann?

why are there different formulas for entropy? (the Boltzmann one and the black hole one given by hawking). entropy by Boltzmann is $S= k \log W$ entropy for a black hole is $S=zA$ where $A$ is the ...
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If information is conserved, why did the early universe had lower entropy than now? [duplicate]

If information and entropy are equivalent, and information is a conserved quantity because of unitarity, what does it mean to say that entropy is growing since the big bang (I know why it grows, I'm ...
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Finding an expression for isothermal compressibility from entropy $S(E,N,V)$

I am trying to find a way to find an expression got the isothermal compressibility ($\kappa_t$) and for the thermal expansion ($\alpha$) of a cristal that has an entropy function S(E,N,V). The entropy ...
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Where is the error in this change of entropy derivation?

The thermodynamic definition of entropy is $\mathrm{d}S \equiv \frac{\delta Q_{\mathrm{rev}}}{T}$ where $\delta Q_{\mathrm{rev}}$ is a strictly reversible "change" in heat. The second law of ...
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What is state variable and full differential? e.g. in entropy?

I am studying basic concepts of entropy and statistical physics. And red a lot what is entropy, and that it is integrative factor of heat; and getting it with the full differential._ Anyway, what I ...
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Exergy, entropy and energy quality

I'm teaching a class on the subject of "energy quality". I'm supposed to tell them that energy quality is a measure of how easily (effective I guess) the type of energy can be converted to different ...
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Why can't we plot irreversible processes on a $T$-$S$ diagram?

In the book "Heat and Thermodynamics" by Zemanky, It is stated that "only reversible processes can be plotted on a $T$-$S$ diagram. Since the definition of entropy involves a reversible change in ...
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Entropy theorem $S(\rho)>\theta S(\rho_1)+(1-\theta)S(\rho_2)$

Considering the definition of entropy: $$S(\rho)=-k_b Tr(\rho\log\rho)$$ Let the statistical mixture of states: $$\rho=\theta \rho_1+(1-\theta)\rho_2$$ I know the following theorem is valid: $$S(\rho)&...
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Is time travel a violation of second law of thermodynamics?

According to the increase of entropy principle, the entropy of the universe is always increasing. So, does going back in time violates the second law of thermodynamics? Because entropy of the universe ...
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Energy and entropy in a system with parts which are thermally isolated

I am going through the Gibbs' paper "On the Equilibrium of Heterogeneous Substances" and in the beginning of the paper, the following is written: If the system consist of parts between which there ...
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Question about thermodynamics

The Second Law of thermodynamics allows work to be transformed fully into heat, but forbids heat to be totally converted into work. If heat could be transformed fully into work it would violate the ...
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What is the entropy of a glass of water?

I have some idea what entropy is, but how much is it? It should be a property in $JK^{-1}$, but what is its size? Is it in $10^{15}$, $10^{20}$ or what? For example for a $100ml$ glass of water at $...
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Total Reversibility of Carnot Cycle

I was reading about Carnot cycle in "Thermodynamics by Cengel & Boles", now it is stated that Carnot cycle is a totally reversible cycle, i.e it is an internally as well as externally reversible ...
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How would I calculate the maximum complexity of living system based on entropy increase acceleration? [closed]

Living systems locally decrease their own entropy by increasing the entropy of their environment by larger margin, creating a local minimum in entropy. The higher the complexity of the living system, ...
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Why does taking work from a system not reduce its entropy?

In Daniel Schroeder's book Thermal Physics, he makes the point that as energy is put into a system it's entropy goes up (there are some exceptions to this generally, but for this question we can ...
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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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Lower bound on quantum relative entropy

In my research this summer, I have become interested in lower bounds on the standard "Umegaki quantum relative entropy". For two non-negative matrices $X$ and $Y$, the Umegaki quantum relative ...
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Quasi Static Reversibility Theorem

As far as I know, the definition of a reversible process is simply "a process that can be reversed". Meaning, that for an isolated global system containing the subsystem in question, its thermodynamic ...
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Confusion about entropy when applied to the whole universe. What are the macrostates?

I'm really confused about the concept of entropy when applied to the whole universe. The often hear that the universe started with very low entropy and as the entropy increases the universe will ...
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If entropy is a measure of disorder, how come mixing water and oil finishes in a well ordered, separate state? [duplicate]

By the second law of thermodynamics, entropy tends to increase when the system is let on itself. And if entropy is a measure of disorder, how come mixing oil in water and letting the system reach ...