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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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 ...
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Relation between entropy and internal energy

I am confused as to what is the relation between entropy and internal energy. Entropy is always presented as a measure of the randomness in a system. So when we supply heat to a well insulated system ...
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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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Books on entropy [closed]

What books introduce entropy in a intuitive, elementary way (at most, for a person with undergraduate physics studies)? The book should not necessarily introduce entropy in relation only to ...
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Accessibility by reversible processes and the Second Law of Thermodynamics

One common way of motivating the existence of Entropy as a state function is the following. Let us take the Clausius/Kelvin-Planck statement of the second law, from which we can deduce Clausius' ...
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Change in entropy of thermodynamic environment during isobaric or isochoric processes

When an ideal gas follows a isobaric or isochoric transformation (no matter if it is reversible or not) I'm not sure what is the change in entropy of the thermodynamic environment. First of all, ...
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372 views

Is information entropy the same as thermodynamic entropy?

Context In one of his most popular books Guards! Guards!, Terry Pratchett makes an entropy joke: Knowledge equals Power, which equals Energy, which equals Mass Pratchett is a fantasy comedian ...
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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 to Atmosphere. How to find entropy production of opening the windows in the winter? where the ...
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294 views

Why would a Boltzmann brain be transient?

The Boltzmann brain idea as I understand it: suppose the universe has an infinite lifetime. Once heat death is achieved, there are no more large-scale structures to the universe -- everything is just ...
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52 views

Entropy and Clausius inequality

From the Clausius inequality we can derive that the efficiency of a Carnot (reversible) cycle is given by: $$e= 1 - \frac{T_c}{T_h}$$ Is this true for every reversible cycle? Is the efficiency of all ...
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63 views

Does conservation of information mean that the direction of causality is arbitrary? [duplicate]

If it is the case that the information content of the universe is conserved, and the past can be constructed from a complete knowledge of the future just as easily as vice versa, then is there any ...
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If a flywheel is spinning at say 1,000 rpm, would an input of 500 rpm would actually slow it down? [closed]

When a flywheel is stationery, an input of 500 rpm would translate to less than 500 rpm in the flywheel considering entropy, but what happens if the flywheel is already running at 1000 rpm, wouldn't ...
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Home Work Help: Calculating Entropy for Melting Ice - Clarification on answer

The question states: What is the change in entropy for the process to completely melt 8.0 kg of ice at 0°C? The formulas for Entropy we've been introduced to are: ...
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39 views

Entropy change in mixture of two gases

I'm confused about the entropy change if two gases, initially separated, are mixed togheter in a rigid box. I use the following $$\Delta S_1= n_1 c_{v,1} \mathrm{ln}( \frac{T_f}{T_{i,1}}) + n_1 R \...
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Should entropy define order rather than disorder? [closed]

Disorder, as I understand it, is basically a measure of entropy. This does not seem correct to me, and appears to be a result of our macroscopic bias. Not only does the beginning of the universe ...
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71 views

The Correct Statement of the Third Law of Thermodynamics

The Third Law of Thermodynamics can be stated in various ways, one of which is: The entropy of a perfect crystal at absolute zero is exactly equal to zero. Is this true for only "perfect ...
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What is the relationship between an expanding universe, an increase in entropy and the the creation of mass?

What is the relationship between an expanding universe, an increase in entropy and the the creation of mass? Could the creation of mass be driven by or in equilibrium with the creation of space?
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Why Boltzmann Entropy's formula is $k_B\log\ W$ and not $0.5\ k_B\log\ W$?

This question is probably wrong - however, I wish to understand even why it's wrong.. Let's take the monatomic gas situation. By the Equipartition theorem, we have that for every degree of freedom ...
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68 views

Can an adiabatic, isentropic transformation be irreversible?

My question is very similar to this, but I decided to ask another question because I felt that the problem deserved to be addressed in a more specific and formal way and I also wanted to discuss a ...
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1answer
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As I understand it, entropy (and disorder) always increase, but gravity increases order. How does physics explain this?

Examples of ordering by gravity: The disordered cosmic dust collects into planetary systems. Planets collect the heavier elements at their cores and the lighter elements above. On Earth, iron ...
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How much of water's surface tension is entropic?

Water molecules on the surface of an air-water interface have preferred orientations that lower their energy. This implies that these molecules are not uniformly distributed in orientation space, ...
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Experimental confirmation of the textbook explanation for local entropy reductions

Clarification: In my original wording of this question, regrettably, I did not make it clear that I am interested in the the Boltzmann/Gibbs/statistical (BGS) interpretation of it, as opposed to the ...
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Adiabatic piston: why is Callen's argument flawed?

This question is related to this one. I would ask you to read that question and my answer to the question itself before answering this one. The problem is the following. In his book Thermodynamics, ...
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1answer
34 views

Is Entropy Maximized, or Just Increased?

Do different real processes involve different rates of change of entropy? (Is the rate of change of entropy constant with time throughout all regions of space, or perhaps in other words, constant with ...
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Effectiveness of phase-change materials vs water for heat storage?

I'm trying to understand the benefit of specialized phase-change materials vs. water for absorbing heat in a home during the day. It's my understanding that selecting phase-change materials whose ...
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1answer
124 views

Von Neumann entropy of mixtures of coherent states

I'm trying to calculate the Von Neumann entropy of statistical mixtures of coherent states. The problem is that such states are in general non-Gaussian, so one cannot follow the formalism developed ...
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Does the Lyapunov exponent and Entropy change? [closed]

If $\lambda$ is the largest positive Lyapunov exponent of a piecewise linear dynamical chaotic discrete in time map, then is there a relationship between the entropy and its $\lambda$. In the paper ...
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Do gravitational waves have entropy?

We know, according the current understanding of black holes and General Relativity, as well as quantum fields in General Relativity, that black holes have an entropy proportional to the area of the ...
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32 views

A system with temp T is in contact with a reservoir of temp T. Would the system ever take in energy and expand (do work) in this situation?

The context is explain a Carnot cycle and how to get work from a system. Its starts by saying the system is in equilibrium with its surroundings, but then it take in some energy Qin. How does ...
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1answer
47 views

Why does stagnation pressure reduce across a normal shock?

I am seeking an explanation for this graph where the subscript "1" refers to the supersonic region and the subscript "2" refers to the subsonic region present beyond a normal shock. The static ...
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Entropy of unattended music streaming and other useless processes

I just realized that on my work pc, I had an internet music streaming service turned on for the last week, but muted (=useless). I was wondering how much entropy in excess was generated by ...
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Understanding Gibbs $H$-theorem: where does Jaynes' “blurring” argument come from?

According to this Wikipedia article, the $H$-theorem was Boltzmann's attempt to demonstrate the irreversible increase in entropy in a closed system starting from reversible microscopic mechanics. ...
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Collapse of two large black holes in AdS

In $4d$ flat space, two black holes of mass $M$ can collapse to form another one of (roughly) mass $2M$. This process is spontaneous, as reflected by the fact that the black hole entropy $S=M^2$ ...
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Intelligence and Entropy [closed]

Is intelligence an entropy transformer? and the difference between a lower and higher intelligence is the efficiency?
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Can black holes grow via accretion of dark matter particles?

I'm assuming that the answer to the question in the title is a resounding yes. Since Baryonic matter and dark matter interact via gravitational forces. If this is the case how is information not lost ...
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Is it possible for a system to become irreversible?

Imagine a ball bouncing in a box for a long time. We know, there is a certain path it can go to bounce off infinitely (see the image). If it gets to this state, it will never be able to get back again....
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Does entropy always increase with temperature? [duplicate]

For any system can we always say that entropy increases with temperature. In other words: $$\left(\frac{\partial S}{\partial T} \right)_{\{\alpha\}}\ge0$$ where $\{\alpha\}$ is the set of parameters ...
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The calculation of the entropy of a single atom

I used to think that the entropy of a single atom could not be calculated, for in my mind only the entropy of a system containing many atoms could be calculated. But my professor told me the entropy ...
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1answer
63 views

If Black holes are maximal entropy how can they evaporate?

According to Hawking/Bekenstein a black hole represents the highest amount of entropy for a given volume, (actually the entropy is related to the surface area of the black hole but the fact that they ...
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Entropy always increases in a closed system - what if the universe is open?

An interesting question I was asked: Entropy always increases in a closed system - what if the universe is open? Does that mean that entropy can decrease in such a system? Of course, I think there is ...
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Gravitational entropy [duplicate]

In the beginning (big bang), mass was evenly distributed (if you consider an elementary particle as an extended object, like a circle on a very thin cylinder, with a radius near the Planck length, but ...
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102 views

What ds>dQ/T mean?

I read the derivation on page 216 over here: https://www3.nd.edu/~powers/ame.20231/notes.pdf First it considers an irreversible process between state 1 and 2 followed by a reversible process between ...
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Entropy for $N$ number of particles [closed]

If there are $N$ number of non-interacting and distinguishable particles which have either Energy $E_1$ or $E_2$ , then a. What will be the entropy $S(n)$ for such system? ($n$ is the number of ...
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Increase in entropy principle

If we consider a system to undergo an irreversible process from state 1 to state 2 and a reversible process from state 2 to state 1, then through Clausius inequality $\int_{1}^{2} \frac{\delta Q_{...
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Extensiveness of entropy in classical microcanonical ensemble

In introducing microcanonical ensemble of classical statistical mechanics one pretty much starts by postulating that entropy of the system has the form $S(V,E) = k \log \Gamma(V,E)$, where $\Gamma$ ...
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Can the second law of thermodynamics be violated in a small enough system if tried repeatedly enough?

Second law of thermodynamics is observed in the universe because statistics favors it, right? And in large enough system this statistical tendency becomes certainty. Does it also mean that negative ...
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What processes create or destroy information?

From a classical standpoint, it seems pretty clear that information can be easily lost. If you knock over a bookshelf and the books fall out, it seems like their initial order on the shelf cannot be ...
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Why does hot water gets cooler on stirring instead it should have gotten hotter

When we keep on stirring hot water vigorously it starts getting cooler. But we are increasing the random kinetic energy of the molecules of water. Heat is as it is the energy of RANDOM motion of atoms....
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Is there a way to prove information entropy?

Information entropy is a very general term involving everything from the tendency of material to decay (in all the 3 meanings) to the fact that you need energy to sort your books alphabetically. Let'...