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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What does the no-hair theorem state about the entropy of black holes?

So does the no hair theorem say that all classic black holes will have zero entropy? If yes, why?
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Boltzmann or Gibbs entropy for the canonical ensemble?

For the microcanonical ensemble the entropy, is given by the Boltzmann entropy which equals: $$S = k_\mathrm{B} \ln(\Omega(E))$$ where $k_\mathrm{B}$ is Boltzmann's constant and $\Omega(E)$ the number ...
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Does a pure quantum state has zero entropy also in the real world? [duplicate]

I just read the statement that a pure quantum state has zero entropy. It appears that in theory, this is correct; but in practice, it is not, because there is always some mixing with the environment. ...
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What are some examples of microscopic quantities?

Mass, volume, energy, entropy, temperature, pressure are some macroscopic quantities. Which means we can think of them even without considering the molecular nature of matter. What are some examples ...
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If in principle all processes are $TPC$ symmetric then what causes the direction of time?

Let's assume all processes are TPC symmetric. Be it the breaking of an egg (just reverse all momenta of all particles involved), the evolution or collapse of the wavefunction (a big if but let's ...
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What's wrong with my argument about entanglement entropy in QFT being time-independent?

Let's say we need to compute the entanglement entropy (EE) of a subsystem $A$ ($A=[0,L]$, $L>0$) in a 2D CFT. The density matrix of the total system (i.e., the real axis) is given by $$ \rho(t)=\...
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Do irreversible thermodynamic processes CONSTITUTE time or do they MOVE IN time? [closed]

Time can be associated with irreversibility. A broken egg can't reassemble. Most, if not all, processes are irreversible and this is associated with time going in one direction. Ŕemarkably, living ...
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Are complexity and disorder correlated in entropy?

I am coming from the musical field, but I am looking into the topic of entropy. In many articles from the field of physics, I keep finding what I consider a sort of misunderstanding, but I may be ...
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Isolation vs the Minimum Energy Principle

The Second Law of Thermodynamics says, that in equilibrium the Entropy S of an isolated system is maximized. The First Law of Thermodynamics says that an isolated system has fixed internal energy U. ...
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It seems that enthalpy is maximized at equilibrium

For a closed system at constant pressure $dH=TdS+VdP=TdS$. On the other side we have that $dS \ge \delta Q/T$ that is $TdS \ge \delta Q$. So we have $dH \ge \delta Q$ and if the transformation is ...
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Conservation of information in expanding universe

As the observable universe expands the amount of information is increasing, at least locally. How is this compatible with the conservation of information in quantum mechanics?
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Would Maxwell's demon having infinite memory storage break the second law of thermodynamics?

Apologies if my understanding is wrong, I am literally a child. Maxwell's demon is meant to break the second law of thermodynamics by making a disorderly system orderly (see image below). But the ...
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Entropy of a deterministic reversible system

Suppose a deterministic reversible system evolving from state A of gas located in a small bottle in an otherwise empty room, to state B where the gas is dispersed throughout the room. Why is the ...
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Iterative calculation of Entropy increase when Bottle A charges Bottle B [closed]

I’m doing a classical problem in an iterative manner on a spreadsheet. This is a trial for a more complicated study. As shown in Figure 1, at each opening of the valve, 0.0784 Kg of air (denoted as ...
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Computation of two-site entanglement entropy of the critical transverse-field Ising chain

The paper Osborne and Nielsen, Phys. Rev. A 66, 032110 gives an exact solution for the two-site reduced density matrix for the transverse-field Ising model with periodic boundary conditions (Eq. 26): $...
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Could the passage of time be sinusoidal? [closed]

As we know the universe is moving towards an equilibrium, or high state of entropy. From what I understand, we call this the flow of time. When google announced their time crystal, they call it "...
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Weinberg's proof of Gibbs' $H$-theorem

I'm trying to understand Weinberg's explanation of a general $H$-theorem he attributes to Gibbs (Foundations of Modern Physics, p. 35), but I'm having trouble with the mathematical modeling. The goal ...
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Entropy of a non isolated system [closed]

I'm trying to self study thermodynamics. I've stumbled upon a problem on my textbook (which is italian by the way): a real thermal machine based on a Carnot's cycle works between two sources of ...
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Interpretation of thermodynamics applied to whole universe gets me confused… [closed]

While thinking about thermodynamics, I was confused about the interpretation of its fundamental concept. If we assume the whole universe as a thermal system, and describe all energy transfer as a ...
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Conceptually, why is the entropy of black hole related to Planck length?

I was watching a lecture on the holographic principle, and it presented the equation for the entropy of a black hole as $$S_{BH} = \frac{A}{4l_p^2}$$ My question is why, conceptually, the entropy of a ...
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How much information can be stored in a system with synthetic dimensions?

Okay this is a completely serious question and keep in mind I have a PhD in theoretical condensed matter physics, in which I have somewhat of a specialization in Floquet physics. So as the title says, ...
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How can Entropy be maximal when it is undefined everywhere else?

This question is about classical thermodynamics. I learned that when an isolated system is not in equilibrium, its thermodynamic variables such as Entropy are undefined. I also learned that when an ...
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Entanglement entropy of the infinite transverse field Ising chain at the critical point

Consider the $1$D transverse-field Ising model, $$H = -\sum_i \sigma_i^z \sigma_{i+1}^z-h\sum_i \sigma_{i}^x$$ at the critical point $h=1$ with periodic boundary conditions. Question: What is the (von ...
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Entropy density and field theory

How does Entropy density depend on Temperature in the $d+1$ dimensional Field theory? Does it always vary as the space power of Temperature, i.e. $s(T) \propto T^{d}$? If so, why?
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Why is rapid expansion/compression reversible?

I am looking over the Otto Cycle on this MIT website and it says at one point "the processes from 1 to 2 and from 3 to 4 are isentropic" in reference to the expansion and compression of the ...
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Why is rapid expansion/compression considered a reversible/isentropic process?

I am looking over the Otto Cycle on this MIT website and it says at one point "the processes from 1 to 2 and from 3 to 4 are isentropic" in reference to the expansion and compression of the ...
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Given infinite inflation would all combinations of particles be likely to occur?

My question is, in the eternal inflation model of the universe, some theories predict that random thermal fluctuations would be likely to form most combinations of matter over infinite time. This is ...
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Quantum extremal surface and black hole evaporation inquiry

Recently there has been progress made in the black hole information paradox by using the tools of AdS-CFT correspondance. Specifically, the Page curve for an evaporating black hole has been ...
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Derive the Gibbs Entropy from Boltzmann Statistics

It is a known fact that we can derive the Boltzmann distribution if we apply the maximum entropy principle at thermal equilibrium. In this post, I am going to work reversely: I want to first assume ...
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Time's Arrow, or Why does time seem to be flowing in one direction? [duplicate]

I have been working on this topic for the past 6 months, and I Understand what is time, but why does it have a direction? Why was the Entropy low in the Early Universe? I have got success in some ...
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Phase Transition in 2D Hard Rods

Consider $N$ rods in a plane with length $2l$ restricted to rotate by an angle $\theta$ leading to excluded volume $\Omega (\theta) = l^2(\theta + \sin\theta)$. Under the assumption that the phase ...
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Swap entanglement from harmonic oscillator chain

I am currently analyzing a system of coupled harmonic oscillators in a thermal state and have already asked a question related to this. I have calculated the entanglement entropy of a chain of two ...
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Entropy of harmonic oscillator in 1d, 3d and anisotropic 3d

I'm curious about the entropy of a simple harmonic oscillator in a few different scenarios: 1d: particle with mass m moving in one dimension, potential $U = \frac{1}{2} k x^2$ 3d isotropic: particle ...
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Entropy of real substances - Is it possible to decompose arbitrary $p$-$V$ cycles of real substances in small Carnot cycles of an ideal gas?

In physics textbooks it is proved that $\oint\frac{δQ_{rev}}{T}=0$ by decomposing an arbitrary cycle in the $p$-$V$ diagram into infinitesimal Carnot cycles. Does the arbitrary cycle have to be a ...
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What is the relation between potential energy and microstates/entropy?

Volume has a clear calculation of entropy: For a change of volume $\Delta V$ for $N$ particles, we have a gain of microstates according to: $$ \Delta \Omega = \Delta V^N$$ So the change in entropy is ...
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Does $U(S,V,N) = \alpha e^{\frac{S}{N c_v}} V^{\frac{c_v-c_p}{c_v}} N^{\frac{c_p}{c_v}}$ really imply zero entropy?

According to this question, for some ideal gas $$U(S,V,N) = \alpha e^{\frac{S}{N c_v}} V^{\frac{c_v-c_p}{c_v}} N^{\frac{c_p}{c_v}}$$ From this, $$T = \frac{\partial U}{\partial S} = \frac{1}{Nc_v}U \...
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How does entropy work with mixing?

Imagine a hypothetical box filled with water, with two equal-volume partitioned sections: one at 40 degrees, and the other at 60 degrees. There is thus an energy associated with the difference in ...
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Is $dS \ge \frac{\delta Q}{T}$ equivalent to Clausius theorem?

If we integrate over a cicle we have $$ 0 \ge \oint \frac{\delta Q}{T} $$ because $S$ is a state function. On the other hand we can prove $dS \ge \frac{\delta Q}{T}$ starting from Clausius theorem. So ...
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Why do we need Legendre transformation for thermodynamic potentials?

I get the idea that thermodynamic potentials are introduced because it is not always easy to describe a system's energy as a function of variables like $S,V,N$ as we normally do with internal energy $...
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What is the intuition of the expected value of the logarithm and entropy?

Gibbs entropy is written as $$ S = -k \sum_i p_i \ln p_i $$ Here is $p_i$ the probability that a system is in a microstate $i$ if I understand correctly. This looks exactly like the expected value: $$ ...
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An extension of von Neumann entropy to observables

Suppose we define the "entropy" of a self-adjoint matrix $\rho$ as the real number $S(\rho)$ given by: $$S(\rho)=-\text{tr}(\rho\log|\rho|)$$ (notice the absolute value on $\rho$, as $\rho$ ...
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Breaking down of 2nd law of thermodynamics [closed]

Do you know a scenario where the second law of thermodynamics breaks down?
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Questions on the Proof of Lemma 1 In Hastings Paper on Area Law

I am currently reading the paper by Hastings on the area law and one dimensional systems. I have some questions on the proof of the first lemma. The proof can be found in the appendix which starts on ...
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Heat Capacity at Constant Volume and Pressure

My thermodynamics textbook (Blundell & Blundell, second edn.) states in equation (16.65) that $$\frac{C_V}{T}=\left(\frac{\partial S}{\partial T}\right)_V \quad and \quad \frac{C_p}{T}=\left(\frac{...
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Doubt in entropy change of environment in an irreversible isochoric process

I have read the following:- The entropy change of the environment is calculated by $\Delta S_{env}=-\int \frac{dq_{sys}}{T} $ for that process. Unlike for a system, we do not assume a reversible ...
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Understanding another Inequality on Entanglement Entropy Found in Hastings Paper on the Area Law

I am currently reading and trying to reproduce the proof found in the following paper by Hastings, in which he proves that the ground state of 1D gapped systems follow an area law. I am trying to ...
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Understanding an Inequality on Entanglement Entropy Found in Hastings Paper on the Area Law

I am currently reading and trying to reproduce the proof found in the following paper by Hastings, in which he proves that the ground state of 1D gapped systems follow an area law. On the second page, ...
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Why is the formula for entropy multiplicative when particles are said to lack haecceity?

The calculation for entropy counts each particle in a potential microstate as an individual. However, I have read in numerous places that physics dictates that we reject the haecceity (i.e. the ...
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How can the Gibbs free energy equation be at constant temperature and pressure?

I have read that the equation $\Delta G = \Delta H-T\Delta S$ is valid only at constant temperature and pressure. However, $\Delta H=0$ in an isothermal process which would give $\Delta G = -T\Delta S$...
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Formulation of entropy distance from equilibrium for fluctuations of the extensive parameters

I am looking for a valid definition/formulation of the distance from equilibrium entropy $\Delta S$, with the request that: $$0 \geq \Delta S \hspace{1cm} (1)$$ The fluctuations in the extensive ...
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