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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How do we explain No change in Entropy in an Adiabatic Quasi-Static Expansion from the perspective of Boltzman's Idea of Entropy?

I understand from the formula of Clausius idea of Entropy that the change in entropy in an adiabatic quasi-static process is zero. I do not understand, how we can explain the same idea from the ...
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Does exponentially decaying correlation imply area law?

In general, for the ground state of a gapped Hamiltonian, we have: For any two local operators $\hat A, \hat B$, they have exponentially decaying correlation: $\langle \hat A \hat B \rangle - \langle ...
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Problem with microstates and corresponding volume in the phase space

I've been struggling without any result on a formal problem about the relation between microscopic states of a system and the volume occupied by a macrostate in the phase space. I'm now very confused ...
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General definition of reversible process without mentioning changes in the environment

I'm looking a general definition of a reversible process for a (closed) system that wouldn't need to say anything about the environment and would be based on the intuitive notion of "reversing&...
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Is the Energy Associated with the Loss or Gain of Information Dependent on Temperature?

I believe it was Leo Szilard who derived a relationship between entropy and information: /S = k ln(2) where k is Boltzmann's constant and /S is the change in entropy of a bit of information. If each ...
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Entropy of an isolated system

It seems that entropy of a system is related to the fluctuation in total energy due to exchange with the environment. But in an isolated system, there can't be any fluctuation, which would imply zero ...
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How to prove that a set of derived closed-form equations for a heat exchanger do not violate the second law of thermodynamics?

Recently I have been working on a problem involving a cross-flow heat exchanger (Two fluids flow orthogonal to each other on either side of a separating wall and exchange heat with each other through ...
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Entropy always increases. Then why did elementary particles come together to form an atom?

It is generally said that entropy always increases. But after the Big Bang elementary particles came together to form an atom. Isn't that paradoxical ?
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How was information generated in the early universe?

Since according to the unitarity principle of quantum mechanics the total amount of information in the universe is conserved over time, how was this information generated in the first place? And how ...
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Are there particles that carry time? [closed]

As every event in the universe can be reduced to interaction between particles via the 4 fundamental forces, can the same be applied to time? Could the flow of time be reduced to a particle that ...
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Is it possible to break the second law of thermodynamics regarding entropy? [duplicate]

The motivation behind my question is that it seems very unlikely that a chunk of metal would "randomly" reach escape velocity and fly away from the Earth, but it happens thanks to NASA and ...
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Double slits experiment: how does the which-way entropy vary with the distance between slits and screen?

When the screen is just behind the slits we have perfect which way information. The entropy is log 2. It decreases if I place the screen in the Fresnel region (not to far). It decreases much more in ...
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Question on “The more information you have about a system, the more work you can extract from it”

This was said in the comments (#15/#27) of this Scott Aaronson post about "information is physical" and reaffirmed by Sean Carroll and praised by Scott among others. https://www....
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Why do particles have only one bit of information in the Derivation of the Bekenstein bound

Bekenstein derived the formula for the maximum energy content of a given volume of space by considering forming a black hole from particles each containing one bit of information. Actually what is ...
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Entropy in a system constitute by an atom and a photon

Suppose that we have an atom $A$ in an excited state. This atom has a probability of emitting a photon $\gamma$. If we are in a finite space there is a probability that the atom $A$ absorbs the ...
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Is it possible to localize entropy creation?

When two obects $A$ and $B$ exchange heat irreversibly ($T_A\neq T_B$), the entropy of $A+B$ increases. My question is where: in $A$, in $B$, on the boundary? Is there some entropy exchange between $A$...
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Is a reversible path for entropy calculations always physically feasible?

Alright, so now I understand that entropy is a state function and we can easily calculate it by devising a reversible path between the two states of an irreversible path. For calculating the entropy ...
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Is there a meaning to $\mathrm{e}^{H(p_{i})}$ or $2^{H(p_{i})}$?

In my research I find an equation featuring the "exponential entropy" term $\mathrm{e}^{H(p_{i})}$ and I wonder if it has a specific meaning. I have only found rare references to that term (...
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If entropy only increases, at what point was it at its lowest value?

Non-physicist asking. Assuming the origin of the universe of your choice: If entropy only increases, at what point was it at its lowest value? Why? Was this value ever zero?
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Definition of reversibility for a non-adiabatic process

I would like to find a clear definition for the following expression: System A undergoes a reversible transformation when the transformation is not adiabatic (when system $A$ is not thermally ...
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Child Universes

I was watching a program on the future of the Universe and it got into the eventual heat death resulting from Hawking Radiation as the last hurdle till nothingness (assuming the unproven theory of ...
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Maximizing entropy with Lagrange multipliers

This is a problem I saw in a stat mech textbook, and I think it is a fairly common problem. Given the entropy function: $$S = - \sum_{i=1}^N p_i \log p_i$$ Maximize $S$ subject to constraints: $$ \...
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What features do reversible work have over the irreversible kind?

At 6:47 of this video lecture, the professor defines enthalpy for a constant pressure process as $$ q_{p}= \Delta U + p \Delta V$$ but, I can not understand why the work he implicitly starts referring ...
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Matrix Exponential [closed]

i'm working on a paper about quantum entropy and i'm stuck on an analytical step about computing a matrix exponential. I have the following Hamiltonian $$H=\frac{1}{2}\sum_ip_i^2+\frac{1}{2}\sum_{i,j}...
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Statistical mechanics definition of temperature as the average kinetic energy

In most text books of statistical physics, temperature is defined as : $$T=\left(\frac{\partial E}{\partial S}\right)_V$$ where $V$ stands for any external variable(s) the system's Hamiltonian depends ...
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Is Gibbs free energy not zero always? [duplicate]

The heat q we provide is change in enthalpy. Also we measure entropy by the heat we provide with respect to Temperature(S=Q/T). In gibbs equation, dG= dH-TdS dH is the energy we supply. Also TdS is ...
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Temperature of air coming out of a tyre due to a burst

I saw several questions where I had to calculate the temperature of the air coming out of a tyre due to a burst, given the external atmospheric pressure and the initial state of the gas present in the ...
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Is the entropy model fundamentally wrong? [closed]

By a popular definition, "entropy quantifies the number Ω of microscopic configurations (known as microstates) that are consistent with the macroscopic quantities that characterize the system (...
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Is there a tabulated reference for CO$_2$ reactions showing entropy and free energy?

With all the climate change attention I am hoping to find a CO$_2$ reference that can help me find a $\text{CO}_2$ reaction with $\Delta \text{S}^{\circ}$ less than zero, and ideally $\Delta \text{G}^{...
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Introductory References for the Black Hole Information Paradox

I am looking for introductory references for the Black Hole Information Paradox and trying to compile a sequential list through which someone familiar with the basics of QFT and GR can go to ...
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How does String Theory calculate the entropy of a black hole in a background-dependent way?

How does string theory get an agreement to the Hawking-Bekenstein equations to calculate the quantum entropy of a black hole in a background-dependent way? Is there any sort of area parameter in ...
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Given a random distribution of matter in the universe, what's the frequency of permutations of ordered matter?

I know matter isn't purely randomly distributed since it clumps together from various forces acting on it constantly, but I just want to discuss randomly distributed matter. Unless, there is a way to ...
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Does entropy change with Reynolds number?

It seems like, as a flow becomes more turbulent, there should be more possible states in the fluid. Shouldn't that correspond to an increase in entropy? Steam tables seem to only depend on temperature ...
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Question about thermal radiation and the 2nd Law

I am studying thermal radiation and considering two radiating black bodies. The book describes the net heat flux as the difference between the flux from object 1 to object 2, and the flux from object ...
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Max-relative entropy between a state and its marginals

Background The quantum relative entropy is defined for any quantum states $\rho, \sigma$ as $$D(\rho\|\sigma) = tr(\rho\log\rho) - tr(\rho\log\sigma)$$ For arbitrary choice of $\rho,\sigma$, the ...
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Interpolation in a Mollier diagram

I'm currently going a little more in depth with thermodynamics and I'm trying to familiarise myself with Mollier's diagram. What I don't understand is how to read precise values given the initial ...
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Is Carnot cycle the only “most efficient” cycle? [duplicate]

In all the books, that I have studied so far, they say that Carnot cycle is the most efficient cycle. But why isn't any other reversible process as efficient as Carnot cycle? Can somebody please ...
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Boltzmann entropy of Gaussian distribution

Recently I have been looking into different definitions of entropy and came across Boltzmann (unconditional) entropy: $S=-\int_{R} dx \;p(x) \ln p(x)$ I have tried to calculate entropy of regular ...
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How can you determine if a process is possible or impossible by using the 1st and the 2nd Laws of Thermodynamics? [closed]

How can you determine if a process is possible or impossible by using the 1st and the 2nd Laws of Thermodynamics?
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What is the physical meaning of ΔG = q(irr) - q(rev)?

Why is change in enthalpy ΔH equal to heat exchanged following whether reversible or irreversible path whereas TΔS is equal to the heat that would be exchanged if the process was reversible? What is ...
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Can entropy ever decrease in an isolated system? [duplicate]

Consider the simplest such system: a gas-filled chamber. I understand that, were all the gas particles concentrated in one corner, the entropy of the chamber will be lower than the entropy of the same ...
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Discrete Gibbs free energy

Is it possible to define discrete (informational) Gibbs free energy by analogy with Shannon entropy? This is about cellular automata, in particular on a network. We can easily calculate entropy of ...
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A form of entropy for pure states?

A previous question that I asked made me realize I had some major misconceptions about entropy. If I now understand this correctly, given the density matrix of a system, we can calculate Von Neumann ...
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In the theory of open quantum systems, what is really meant by *information backflow* from the environment to the system?

In the context of an Open Quantum System (OQS) i.e. a quantum system coupled to a quantum environment, what is really meant by information backflow from the environment to the system? I'm newly ...
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Maxwell Coexistence from Entropy Considerations

As explained by Maxwell, (1875), a realistic thermodynamical system will, at low temperature, have pressure vs. volume curve that is non-monotonic. In practice, though, the observable states of the ...
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Variation of entropy in a transference of heat

When we put two bodies with different temperatures in contact, there will be a heat transference between them. The variation of the entropy of the system is well known (this is computed in most ...
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2D Ising model entropy as a function of external field

I am trying to figure out what is the entropy expression as a function of the external field in a 2D Ising model with nearest neighbour interaction. My Hamiltonian is the following: $\mathcal{H}=-\...
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Is it possible to have a negative density matrix, and how would you calculate entropy?

I am trying to calculate the Von Neumann Entropy of a quantum state. Given a state $ | \psi \rangle$, I am calculating the Von Neumann entropy by doing the following: $$ S = -\mathrm{tr}(\rho \ln(\rho)...
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Entanglement Measure for 4 qubit?

Given a 4 qubit (pure) state, $|\psi\rangle \in \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2 $, is there an entanglement measure to determine how much these four qubit ...
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Could a cloud of hydrogen-1 or helium-4 turn into Bose–Einstein condensate when the universe reaches maximum entropy?

Laboratories can cool clouds of hydrogen-1 and helium-4 respectively into Bose–Einstein condensate (BEC), while hydrogen-1 makes up 75% of all atomic matter in the observable universe and helium-4 ...

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