# Tagged Questions

A 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 is entropy really?

On this site, change in entropy is defined as the amount of energy dispersed divided by the absolute temperature. But I want to know: What is the definition of entropy? Here, entropy is defined as ...
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### Proving that the Boltzmann entropy is equal to the thermodynamic entropy

I've been trying to understand how we can equate the Boltzmann entropy $k_B \ln \Omega$ and the entropy from thermodynamics. I'm following the approach found in the first chapter in Pathria's ...
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### Free expansion of an ideal gas

I am having trouble understanding the transient phase of an ideal gas expanding into vacuum. Firstly, the pressure of any gas is defined only when there is an instrument (barometer/ wall/ piston) ...
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### Which temperature does $T$ in Clausius inequality ($\oint \frac{\delta Q}T\le 0$) refer to?

I got a little confused about the temperature in Clausius inequality. As you can see in this answer of Luboš Motl, it seems that temperature is the temperature of the system. But in some answers of ...
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### Is the reciprocal of Entropy easier to understand? [on hold]

"A thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system." ...
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### Please explain entropy curve [closed]

I saw this curve at a website, but I didn't understand it. What is the lower point of entropy, and what are the points A, B, and C? Thanks!
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### How to find entropy production of opening the windows in the winter?

Every time you open the windows in the winter (to bring in healthy and fresh air), room's warm air goes outside into Atmosphere. How to find entropy production of opening the windows in the winter? ...
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### Entropy of the cosmological constant and the laws of thermodynamics?

Convention The convention being used is: $A_{C} =$ The classical variable Premise Consider the following toy-model universe: A universe with a positive cosmological constant. Basic ...
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### Reference: authoritative reference on Gibbs and Boltzmann's entropy

Can someone reference a good, standard textbook on thermodynamics or quantum mechanics that explicitly states the formula for Gibbs and Boltzmann's entropy (or maybe Shannon as well)? I am asking ...
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### What Postulate States Entropy must be Positive?

I've been reading the Postulates of Classical Thermodynamics, and I haven't found anywhere to be said that the Absolute Entropy of a system has to be a positive number. The third one states that the ...
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### Meaning of the Reduced Density Operator

I am confused about what it is exactly that a reduced density operator describes. To illustrate, I came across the following seemingly paradoxical argument. Consider a bipartite system $AB$, ...
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### Black hole no-hair theorems vs. entropy and surface area

I was revisiting some old popular science books a while ago and two statements struck me as incompatible. No-hair theorems: a black hole is fully-described by just a few numbers (mass, spin etc) ...
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### How do you prove $S=-\sum p\ln p$?

How does one prove the formula for entropy $S=-\sum p\ln p$? Obviously systems on the microscopic level are fully determined by the microscopic equations of motion. So if you want to introduce a law ...
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### Maxwell's Demon bug, trapdoor space and time

What about the size of the door (space) and how long has it to be opened (time)? I think Maxwell's demon would have a problem with space, if the door is too wide (more than one particle size), then ...
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### Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution?

Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution? I have never seen dissipation explained, although what I have seen a lot is descriptions of ...
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### What is this entropy-related thermodynamic concept called?

I'm trying to sharpen my understanding of a thermodynamic concept. Suppose I've got an idealized building whose interior is held at 10 degrees cooler than the outside air by a heat pump that consumes ...
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### Why doesn't this violate the 2nd law of thermodynamics?

Consider an ideal gas in a cylindrical container in a gravitational field, with a piston on top pushing down by gravity. The piston has some locking mechanism that locks it in place if it is displaced ...
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### Quantum Discord and entropy

I'm trying to understand certain aspects of Quantum Discord. The idea is that a quantum system might have non-classical correlations despite it not being in an EPR-like state. So the discord is ...
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### Maxwell's Demon Constant (Information-Energy equivalence)

New Scientist article: Summon a 'demon' to turn information into energy The speed of light c converts between space and time and also appears in $E=mc^2$. Maxwell's Demon can turn information ...
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### Entropy and probability

I read "The NEW world of Mr. Tompkins" and I'm not sure with one of the Gamow's equation. When he calculated the probability of entropy, he used this reasoning: "How likely is a situation that all the ...
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### What is the meaning of Boltzmann definition of Entropy?

I would like to ask if someone knows the physical meaning of Boltzmann's definition of entropy. of course the formula is pretty straightforward $$S=k_b\ln(Ω)$$ but what in the heck is the natural ...
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### Prove all reversible heat engines that work between just two temperatures have the same efficiency

Can someone explain this explanation to me: A completely different argument focuses on the requirement that the device only move heat at one or other of the two temperatures. Then, provided ...
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### Entropy change in an irreversible process between 2 equilibrium state

Calculating entropy change in an irreversible process between 2 states requires computing the change in entropy for any reversible process between the 2 same states, but why? If someone could provide ...
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### free energy and entropy

my understanding of free energy and entropy is that as entropy of a system increases its free energy decreases. As sun has free energy and this energy is being converted to useful work, and its ...
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### Does the radius of the Universe correspond to its total entropy?

I heard a claim that due to holographic principle, the surface area of the cosmic horizon corresponds to the universe's total entropy. As such the initial state had zero surface area and later ...
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### Reversible cycle approximated by Carnot cycles

My textbook, W.E. Gettys, F.J. Keller, M.J. Skove, Physics 1, gives the definition of a reversible transformation as a transformation that can be inverted by effectuating only infinitesimal changes in ...
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### Definition of entropy in thermodynamics

In most textbooks, the definition of entropy in reversible processes on a system $S$ is given simply as $$d S=\delta Q/T.$$ It seems to me this definition is insufficient since it does not specify ...
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### Arrow of time and entropy?

The arrow of time is usually defined by the direction in which entropy increases. In a closed system, if there's a max entropy that the system can reach, does that mean time stops or at least become ...
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### A mass falls to the ground from a height. What's the change of the entropy of the universe?

A mass $m$ falls to the ground from a height $h$. The temperature $T$ is constant. What's the change of the entropy of the universe? It's an example in Carter's Classical and Statistical ...
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### Change in entropy when mixing water at different temperature

Suppose two amounts of water of the same mass, but with different temperature, are mixed. Then the entropy of the hot water decreases, but the entropy of the cold water increases due to heat transfer. ...
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### Entropy Change for a Thermally Isolated System

Clausius' Theorem states that $\int\frac{dQ}{T}\leq0$ for a closed cycle, with equality for a reversible cycle. Suppose we wish to take our system around a closed cycle such that the path from A to B ...
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### Where is the flaw in this machine that decreases the entropy of a closed system?

I was thinking about a completely unrelated problem (Quantum Field Theory Peskin & Schroeder kind of unrelated!) when the diagram below sprang into my mind for no apparent reason. After some ...
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### Why do many people link entropy to chaos?

I understand that, in thermodynamics, entropy has a precise definition (the infinitesimal change of entropy being the infinitesimal heat transfer divided by the temperature), and that in statistical ...
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### How to derive entropy from density of states?

I'm trying to derive the entropy of a black hole, given the density of states of a bosonic string (the details are not relevant). The density of states is $$\omega(E) = E^\alpha e^{\beta E}$$ The ...
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### How is a irreversible process (conventionally) represented on a $T-S$ plane and why cannot it be (really) represented?

A reversible process can be represented on a $T-S$ plane, and the area under the curve is the heat exchanged by the system. On $P-V$ plane a irreversible process is conventionally represented with a ...