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 entropy in a supermarket lower before or after a shopper puts all the things they want to buy into a trolley?

Let's say there's a supermarket selling a hundred different products. Before it opens for the day, the staff arrange all the products into their appropriate shelves. This should be a low entropy state,...
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Neutron Star formation Entropy

When a neutron star forms, is its entropy lower than when it was in the form of the star core. In the case of a black hole the entropy becomes the surface area, so what happens in a neutron star ...
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Entropy change due to a growing plant

Sunlight hitting a patch of the earth's surface causes the sun to lose entropy and the earth to gain entropy and there is a net gain in entropy (Delta S). But if that sunlight causes a plant to grow ...
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How much entanglement does each quasiparticle carry?

The dynamics of entanglement entropy $S$ out of equilibrium can be understood in some regimes from the point of view of the quasiparticle picture: a highly excited state acts as a source of pairs of ...
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The Formula For Entanglement Entropy of an Evaporating Black Hole

I am trying to find a proof for the formula for entanglement entropy of an evaporating Black Hole. It is introduced and used in many papers such as The entropy of Hawking radiation, by Ahmed Almheiri, ...
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Applicabilty of the definition of thermodynamic temperature

I have a question about the definition temperature, given by $\frac{\partial S}{\partial E}(E,V,N) = \frac{1}{T}$ Is this valid only for isolated systems (and not applicable, for instance, to a (...
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Do we have to consider decoupled particles in the computation of $g_{*}(T)$?

I am studying the thermal history of the universe and I encountered the definition of effective degrees of freedom $g_{*}(T)$ defined as $$g_{*}(T)=\sum_{Bosons}g_{B}(\frac{T_{B}}{T})^{4}+\frac{7}{8}\...
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Expressions for Entropy in the Canonical Ensemble

In the microcanonical ensemble, we have the standard Boltzmann expression for entropy: \begin{equation}\label{1} S = k_B\ln \Omega \end{equation} where $\Omega$ is the number of elements of the ...
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Clausius Inequality and Thermodynamic Potentials

One statement of the Clausius inequality is $$dS \geq \frac{\delta q}{T}$$ where $\delta q$ is the exchanged heat. My understanding is that $T$ refers to the temperature of the surroundings rather ...
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Continuum limit of the discrete entropy expression

I understood where the expression of the entropy $S=-k_B\sum p\log p$ comes from. Now I am trying to take this expression to its continuum limit and I want to get the form $$S=-k_B\int\rho \log\rho$$ ...
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Counting Microstates to get the Entropy Generation in Free Expansion of an Ideal Gas

In Elliot and Lira's Introductory Chemical Engineering Thermodynamics on p.134, the authors derive the entropy generated from an ideal gas expanding from a volume V to 2V, by the removal of a ...
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Why is entropy a quantification of the typical fluctuation of internal energy around the expected value?

In different books (one example is Statistical mechanics of learning, by Engel and Van Der Broeck) I stumbled upon an idea which should be elementary, but to me it is not easy to grasp. Entropy can be ...
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When rain clouds are formed, does the entropy decrease?

Water droplets gathered and formed into cloud which gets heavier then does the entropy of the system decreases? If so why 2nd law of thermodynamics allowed it?
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Why is the work here positive and are we using 2nd law for this conclusion?

I am reading a popular article and in one of the lines it says that : "To illustrate this point, consider the familiar gas-and-piston setup, in which the gas of N = 10^23 molecules begins in a ...
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Heat diffusion equation in terms of entropy?

Ok, I am very rusty in thermodynamics. In fluid mechanics books, you can find the heat transport equation in terms of temperature $T$: $$ \rho c_p\left(\frac{\partial T}{\partial t}+\boldsymbol{u}\...
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Entropy of squeezed vacuum state

Objective: I am trying to familiarise myself with quantum entropy for squeezed vacuum states. Context: As a previous excercise, I have evaluated von Neumann entropy $\mathcal{S}(\widehat{\rho})=-\text{...
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Is fuel cell efficiency limited by thermodynamics?

Let's say we have a mixture of oxygen and hydrogen gas, initially at room temperature and pressure. This mixture can be used to perform work: we can burn it, using the resulting heat as a source in a ...
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Does entrophy changes when measuring a quantum spin of an atom?

I am picturing an atom whose quantum spin states are in superposition, after measuring the spin state does the entropy changes? I think of entropy as a piece of information on the state of disorder ...
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Justification for extending Gibbs entropy to non-equilibrium states

I am taking a course in statistical mechanics and have seen the Gibbs, Boltzmann and Clausius formulations for entropy in equilibrium thermodynamic states. And I have seen that it can be shown that ...
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Are all microstates always equally probable? [duplicate]

The Gibbs entropy is given by: $S_G = -k_B \sum P_i log(P_i)$, where the summation runs over all possible microstates. I've seen one of the assumptions for statistical mechanics was that all ...
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Determine the entropy of an ideal bosonic gas

I am struggling with this problem. So we're told that any macroscopic state of a gas can be characterized by microscopic stated of a single particle. We divide the microscopic states into groups. So $...
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How is entropy calculated in a Constant Temperature process, when a gas is compressed from from $p_1$ to $p_2$? [closed]

Entropy for constant temperature process, when instead of volumes, pressures changes from $p_1$ to $p_2$?
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Relation of entropy given in terms of phase space volume vs. multiplicity

I find in the liuterature (e.g. Landau & Lifshitz [1]) that the entropy in a microcanonical ensemble is given as: $S = k_B \log(\Omega),$ where $\Omega$ is the mutiplicity of microstates (Landau ...
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Change of entropy of surroundings in reversible and irreversible processes

I am currently in high school and trying to gain some conceptual clarity on entropy and the second law of thermodynamics which led me to read various answers on this forum and i have referred some ...
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A version of Maxwell's Demon using Norton's dome to erase information for free?

Norton's dome is a thought expriment that shows Newtonian mechanics is non-deterministic. It has the shape of a dome (see exact details of its construction on the linked page) with a rather peculiar ...
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Entropy change due to surroundings?

What is the entropy generated by opening up a vacuum chamber of volume $V$ to the atmosphere? (let's say with some constant ambient pressure $P_{atm}$) I was reading about Joule expansion, but it ...
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Entropy of Schottky defects

We have a crystall with $N$ atoms. A Schottky defect is one of the atoms leaving their points in the lattice and going to the surface with $N' = cN^{2/3}$ possible atom places. I want to compute the (...
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What makes a perpetual motion machine of the second kind actually “perpetual”?

As I understand it, a perpetual motion machine does continuous work without additional energy input. If a perpetual motion machine of the second kind exists, it violates the second law of ...
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Can entropy decrease although extremely unlikely? [duplicate]

Second Law of Thermodynamics From the second law of thermodynamics, the entropy of the universe must always increase. However, most explanations of entropy state that it is the measure of the number ...
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Irreversibility and organisation of trajectories in the phase space

I am currently thinking about the irreversibility paradox. I am not working in this area and my question is certainly not original but I couldn't see it stated in that form yet. I can't grasp how are ...
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Definition of entropy in the canonical ensemble

I am currently following an introductory class on statistical mechanics. This course starts with general notions of statistics (as a reminder), goes over explaining why one would want a statistical ...
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Comparison of entropy change in a system and in a heat reservoir

Lets consider a thermodynamic system at $T_1$ and a heat reservoir at $T_0$, where $T_1>T_0$. The system cools down, i.e. it gives of heat to the heat reservoir (the heat reservoir can be thought ...
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Entropy variables

When we are defining the entropy we have been used two isolated system not a heat bath with a small system, to ensure that entropy is defined as an energy variable dependent. My question why is the ...
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Boltzmann and Gibbs entropy

I am studying a bit about statistical mechanics for a course at my university. My book introduces first the Boltzmann entropy $S = k_b lnW$, and then the Gibbs one, $S=k_b \sum p_i lnp_i$, in what ...
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Why do distributions tend to the one that maximizes entropy?

It appears to be a well-known fact that a probability distribution on phase space will tend towards the distribution that maximizes entropy. The Wikipedia article on maximum entropy states: "The ...
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Change of entropy of irreversible and reversible processes and cycles

Clausius' theorem states that $$\oint\dfrac{\delta Q}{T}\leq 0,$$ $=$ for reversible cycles and $<$ for irreversible ones. For a cycle with two reversible paths connecting points $a$ and $b$, $$\...
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Would entropy increase if I smashed a glass inside the event horizon?

I read that eventually matters that fall into the event horizon will be shredded into fundamental particles and soon ended up in the singularity but if I were to shatter a piece of glass panel into ...
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Why does sunlight have low entropy?

This question is inspired from The Sun is giving us a low entropy, not energy. I accept the claim that sunlight must be a low entropy source of energy, given that it maintains the entropy gradient ...
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How is Weiss mean field approximation actually maximising the partition function of Boltzmann's distribution?

Considering other mean field approximation (e.g. Max entropy approach or $<S_i> = m_i +\delta S_i$ , $\delta S_i \simeq0$), a common approach that I've seen is that of maximising the partition ...
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Reversible processes in thermodynamics [closed]

These are a few basic questions of mine in thermodynamics whose answer I can't find anywhere. $1$. How does a quasi static process serve the purpose of thermodynamic equilibrium?A quasi static process ...
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What is the classical entropy of the Boltzmann-Gibbs distribution?

Computing the entropy of a single particle has a number of pitfalls, however there seems to be a classical definition that should work. This answer provides a definition of temperature for $N$ ...
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1 answer
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Entropy, as state counting [closed]

In Roger Penrose's book "Cycles of Time, An Extrordinary New View of the Universe," in chapter 1.2 "Entropy, as state counting," the author illustrates the second law of ...
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What is the entropy change of a hatching egg? [closed]

Treating the whole egg as the system. On one hand: The egg was only one cell, but when it becomes a full-grown chicken, it becomes a large number of cells, highly specialized to do their own jobs. So ...
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Principal of maximum Entropy (Two ideal gases in mechanical contact) [duplicate]

Consider a container with Volume V. The container is seperated by a non-movable, impearable wall, which allows heat flow. Both subvolumes are filled with an ideal gas. We can obtain informations about ...
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Mathematics behind the thermodynamic arrow of time

Since the thermodynamic arrow of time is related to the second law of thermodynamics, how can I (mathematically) describe the operation of the operator $\hat{T}:t \mapsto -t$ on said law ? In other ...
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Non-isentropic expansion of an ideal gas?

Consider an ideal gas in a piston, where the piston head moves to increase the volume of the piston from $V_1$ to $V_2$. If the piston head moves and $v\ll v_s$ with $v_s$ the speed of sound in the ...
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Can one derive the second law of thermodynamics from von Neumann's equation?

My idea is that from the von Neumann equation i$\hbar\dot{\rho}(t) = [H,\rho (t)]$ one can derive that $\dot{\sigma}(t)\geq 0$, where $\sigma(t):= -$tr $ \rho(t) $ log $\rho(t)$. However, I end up at ...
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Eigenvalues of truncated correlation matrix

Take a Fermionic gapped 1-D lattice Hamiltonian $H=\sum_{ij}t_{ij}c^\dagger_ic_j$ with periodic boundary as an example, and we bipartite it into two subsystems $A$ and $B$, and the eigenvalues of the ...
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Is the entropy for the classical microcanonical ensemble defined... up to an infinite number?

In the microcanonical ensemble all states $(p, q) \in \Gamma$ (where $\Gamma$ is the phase space of a system with $3N$ coordinates) with the same energy have the same probability density. I would ...
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Emergent Entropic Gravity from Quantum Entanglement in de Sitter Space?

Question: Is there already a theory (formula) available for emergent entropic gravity from Quantum Entanglement in de Sitter space? For detailed background information please refer to a recent ...
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