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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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2nd law of thermodynamics and gravity

If I have a container with gas according to my understanding of 2nd law of thermodynamics molecules/particles will not be at one side of the container but if the container gets energy from outside ...
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Measuring the entropy of mixing ideal gases

Suppose I have two compartments of volume V separated by a barrier. Each one has an ideal gas, pure, of N molecules, and with equal pressure and temperature. However, I don't know whether both gases ...
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How does the virial expansion converging, mean that there is no phase transition?

I have a question regarding how the virial expansion relates to phase transition. I watch the lecture https://www.coursera.org/learn/statistical-mechanics/lecture/1a5Di/tutorial-3-algorithms-exact-...
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Is partition function algorithm-dependent or configuration-dependent?

I am reading this resource to learn statistical mechanics: http://blancopeck.net/Statistics.pdf I am trying to learn about the partition function, which as I understand it, is equal to the number of ...
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Can you reverse the arrow of time?

Has there been any attempt to reverse the arrow of time?
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If heated molecules are more disordered, why doesnt it happen spontaneously?

currently, the way I understand entropy is disorder and that it always increases. I therefore have difficulty to understand why don't object heat spontaneously(i.e take in energy from their ...
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Are attempts to extract useful work from spontaneous decreases in entropy an example of Maxwell's demon?

Something I see often in forums discussing future energy sources is perpetual motion of the second kind. Rather than outright denial of the second law, however, they say the fluctuation theorem shows ...
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About Entropy Definition

I quote the coming lines from Igneous & Metamorphic Petrology by Myron G. Best (2003): One statement of the second law of thermodynamics is that spontaneous natural processes tend to even out ...
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Is Entropy Backwards?

Is it weird that everything with a gradient goes from high to low except for entropy? High pressures try to fill in low pressures, high temp goes to low temp, osmosis happens from high to low, etc. ...
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Does Verlinde's entropic gravity relate Hawing radiation to bodies other than black holes?

To the best of my understanding this is the essence of the point he's trying to establish, am I right in thinking this?
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Calculation of heat generated due to friction for air flowing through a pipe

I am currently attempting to calculate the heat transfer when compressed air is flowing isothermally through a pipe with frictional losses. I realise this might seem like an odd question, but I am ...
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Canonical ensemble near absolute zero

In the canonical ensemble for an ideal gas of $N$ bosons, the partition function for $T\to 0$ scales like $$Z\sim e^{-\beta\epsilon_0N},$$ when $\epsilon_0$ is the lowest (non-degenerate) single ...
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Entropy has units of energy-per-temperature; what is the impled relation between energy and temperature?

Entropy has units of energy-per-temperature, e.g. $X$ joules per Kelvin. Can this be reduced to a simple English sentence that describes the relationship between those $X$ joules and 1 Kelvin? For ...
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Where does energy in osmosis come from?

So I get that work is done when a net force converts potential to heat or kinetic. But I also understand that osmosis is driven purely by entropic processes. There is no net force, only a statistical ...
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If a star forms, entropy decreases… but doesn't this require some form of energy?

A cloud of matter has high entropy. In order to form a star out of matter, the entropy must decrease. For this, energy is necessary. Where does this energy come from?
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Why is entropy generation zero at infinitesimal temperature gradient?

First question: Is the question I asked valid in the first place? Is it really true? Second question: If so, is it because the exchanged heat between the bodies between which the temperature gradient ...
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In what ways can entropy of the universe increase?

So far, I have been able to come across two scenarios in which entropy of the universe increases. First, when heat flows at a finite temperature gradient and second, during expansion of air particles ...
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What will the universe be made of at the heat death?

Explain it to me like I'm a five year old. It's the far distant future and the universe has finally come to its heat death. At this point, what will be left of the universe? Will there perhaps only ...
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Entropy production during leptogenesis

Do the out of equilibrium decays of right-handed neutrinos in standard leptogenesis scenarios lead to a net entropy production? Does this entropy production lead to observable effects (like reheating)?...
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Entropy of the ideal gas - How to derive the $S(U,V,N)?$

I'd like to derive the $S(U,V,N)$ function. In the lecture, we were using the $S=k_b \log(\Omega)$, some combinatorics, approximation, $6N$ dimensional spheres, etc. But I'd like to avoid that if it's ...
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Thermodynamics: Calculate heat flow

I was given the following scheme of a power plant: $ {\def\place#1#2#3{\smash{\rlap{\hskip{#1px}\raise{#2px}{#3}}}}} % \place{300}{290}{\begin{array}{c} 60 \, \mathrm{bar} \\ 575\sideset{^{\circ}}{}{\...
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Absolute entropy at 0 K and residual entropy

The third law of thermodynamics states that the absolute entropy of a pure crystalline substance is $0$ at $0\,\mathrm{K}$. In the analysis of chemical reactions this absolute scale is sued to ...
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Calculating entropy for the surroundings the logical way doesn't work

EDIT: I was missing the entropy change due to temperature change and now everything makes sense Suppose I have $n$ mol of an ideal gas in a chamber with a piston with volume $V$ at pressure $P_{1}$ ...
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Entropy and heat death

If elements or particles(can a single particle have temperature) ... have different thermal capacities how can we determine the heath death and why is it identical for everything ?
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Von Neumann entropy in the algebraic approach

In the algebraic approach to QM a quantum system has associated to it one $\ast$ algebra $\mathfrak{A}$ generated by its observables. A state is a positive, normalized linear functional $\omega : \...
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Can we have situations where thermodynamic extensivity is violated?

In thermodynamics, the internal energy $U$, the number of particles $N$, the entropy $S$, etc. are extensive properties. Can there be situations where the extensivity is violated?
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Entropy of water drop

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. However, if the drop of water falls into water, splashes decrease and disappear over ...
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Holographic dualities and strong subbadditivity of entanglement entropy

Recent analysis of inequalities satisfied by entanglement entropy in AdS bulk duals have led to establishing an equivalence between Strong Subadditivity and the Null Energy Condition (NEC) How hard ...
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What sense is there in entropy arguments when the system can't be known to be ergodic?

What sense does "entropy" make in non-equilibrium dynamics? What is its definition? How is the "entropy of the early universe" calculated, for example? And how can the "entropy of the universe" be ...
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What temperature should be taken into consideration when calculating the entropy change?

Introduction In this question I want to know when calculating the entropy change where we take the temperature of the system or the reservoir's and if my thought process is sound. Clausius Theorem ...
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What are entropy and reversible processes really?

I'm confused about the concepts of entropy and reversible processes. Before explaining the definition of entropy, they used the term "reversible process" without defining it formally. Then, when ...
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Can the ideal gas expand adiabatically and irreversely?

Suppose that the ideal gas is expanding adiabatically from the state $(P_1, V_1, T_1)$ to the state $(P_2, V_2, T_2)$ I think this process can be allowed to happen reversibly or irreversibly, but ...
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Entropy change in a reversible adiabatic expansion of ideal gas

Below is P-V curves of 1 mole of ideal gase for temperature 700K, 500K and 300K each. Now I would like to calculate entropy change of the system along the path from (1) to (3), which is adiabatic ...
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Obtaining the number of quanta for a system of harmonic oscillators

So I need to find the entropy of a system made up of two harmonic oscillators having natural frequency $\omega_0$ and $2\omega_0$. The system is said to have a total energy of $E=(n+\frac12)\hbar\...
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Is there an equivalence between Boltzmann entropy and Shannon entropy..?

I have already parse other posts about this subject but none of them seems to answer completely to my interogation [ this interrogation is to put in relation with this question Is there an ...
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Is there an equivalence between information, energy and matter?

Consider the physical world as made of information, with energy and matter as incidentals. This statement must be placed in the context of the holographic principle and the works of Bekenstein ... ...
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magnetic refrigeration and adiabatic processes

Suppose we have a magnetic material that is well insulated from its environment, and we then ramp up the current in a helmholtz coil that encloses the magnet. We then observe an increase in the magnet'...
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What concept expresses the entropy/system_size ratio?

Being entropy an extensive property, I assume that two systems having the same absolute entropy but different sizes (e.g. particles numbers), have in fact a substantial difference regarding its ...
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Computronium and Time Dilation and Bremermann's Limit

I was contemplating computronium the other day and it occurred to me that there might be a point at which the computronium becomes so dense that gravitational time dilation effects would cause it to ...
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How does the lack of information increase as temperature increases?

Suppose one knows nothing about the concept of entropy. How can we argue that the lack of information/ignorance about the system typically increases with the increase in the temperature using the ...
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How to calculate the number of microstates in quantum-mechanical harmonic oscillators (microcanonical)?

So I have the question where a system of two QM oscillators both have energies $\left(n+\frac12\right)\hbar\omega_0$, and the total energy of the system is given to be $E'=\left(n'+\frac12\right)\hbar\...
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Rigorous proof of how does entropy change with the increase in temperature?

When all other thermodynamic variables pertaining to a system are kept constant, how does the entropy $S$ of a system change with the increase in temperature? Does it strictly increase with the ...
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Do black lines exist?

The entropy of a black hole is given as $$S \propto k_B \frac{A}{l_P^2}$$ where $k_B$ is Boltzmann's constant, $l_P = \sqrt{G \hbar/c^3}$ is the Planck length and $A$ is the area of the event horizon ...
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How can the universe's disorder (entropy) be increasing if energy is becoming more uniformly spread?

It's often said that the entropy of universe is increasing and that the universe's energy is becoming more evenly distributed. But intuitively, we say also that entropy is a measure of the disorder. ...
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Usage of the word “entropy”

The physicist and renown television personality described the 2nd law of thermal dynamics this way: "The second law of thermal dynamics is essentially a death warrant. The amount of disorder in ...
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Is Heat Death the only inevitable end?

I have heard about heat death being the most probable end of the universe. But what are the other possible ends of the universe. I also came across a video stating that due to some effect called as "...
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AdS/CFT and finiteness of entanglement entropy in CFT

AdS/CFT duality maps string theory to conformal field theory. String theory confirms Bekenstein-Hawking entropy, and thus the dual CFT must confirm it. However, CFT is still a quantum field theory, ...
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Change of entropy (Theromdynamics)

I have two problems in connection with Change of entropy. 1. How much is the entropy change of 1kg Helium (at 20 Celsius) if the pressure changes isotherm from 200*10^5 Pa to normal atmosphere ...
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Are isobaric, isochoric, isothermal, adiabatic processes reversible if they all take place quasi-statically?

From my understanding so far, I think that a quasi-static process is one where the system is in thermal equilibrium with itself as well as the surroundings and the process takes place infinitesimally ...
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CMB and entropy in the early universe

The Second Law of Thermodynamics states that the entropy of the Universe must increase. When we look a the Cosmic Microwave Background Radiation we see that the early Universe was in thermal ...