Linked Questions
17 questions linked to/from How to derive Shannon Entropy from Clausius Theorem?
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About entropy in Clausius inequality [duplicate]
From what I know, entropy can be derived from Clausius theorem but this theorem put a constraint in the temperature of the surroundings so, how is $\Delta S\ge0$ in an isolated system valid even with ...
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I am confused relating Entropy in statistics with thermodynamics [duplicate]
The thing is in thermodynamics we learn entropy as a measure of energy of a system per unit temperature that isn't available for the system to do work. Again, statistically, entropy is a measure of ...
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Why is the second law of thermodynamics not symmetric with respect to time reversal?
The question might have some misconceptions/ sloppy intuition sorry if that's the case (I'm not a physicist).
I seem to have the intuition that given a system of $N$ charged particles in 3D space ...
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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 and ...
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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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Does a random number generator have real entropy?
In thermodynamics, entropy is defined for gases. Of course, my laptop is not a gas. However, it contains a random number generator and I have seen the word ‘entropy’ being used in this context. Is ...
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What actually are microscopic and macroscopic viewpoints in thermodynamics?
The microscopic viewpoint of studying a system in thermodynamics is the one in which we consider the system on a molecular/atomic/sub-atomic level. (is that even right?)
The macroscopic viewpoint is ...
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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:
$$ ...
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Derive the Gibbs Entropy from Boltzmann Statistics
It is a known fact that we can derive the Boltzmann distribution if we apply the maximum entropy principle at thermal equilibrium. In this post, I am going to work reversely: I want to first assume ...
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Entropy production in non-equilibrium systems: physical interpretation?
I have been learning about entropy production in non-equilibrium systems as developed by Prigogine and others, especially in the context of chemical reactions. I now understand that from the first law ...
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What is the relation between uncertainty and information obtained from a measurement?
For example, if a measurement gives a position with twice the uncertainty as another measurement, how much less information regarding position are you getting? In other words, if uncertainty doubles, ...
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What is the difference between Clausius' entropy and Boltzmann's?
We can only speak of entropy change, $dS$, when I mention Clausius as
$$dS=δQ/T$$
However, according to Boltzmann, entropy is defined as $S=K\ln\Omega$
My question is, is the $S$ according to ...
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Entropy as extractable useful work vs. statistical entropy
Statistical (Boltzmann) entropy of a (thermodynamic) system is defined as
(The logarithm of) the amount of microstates corresponding to the (thermodynamic) macrostate of the system.
So, in way of ...
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How to conceptualize the unit Temperature?
For a long time, I was under the impression that Temperature is just a shorthand for the "average energy" within a system, but I discovered this is wrong (although sometimes this is a valid ...
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Boltzmann vs Gibbs definition of entropy [duplicate]
I am learning Statistical Mechanics and I have a question regarding different definitions of
(statistical) entropy. If we use Boltzmann's definition:
$$\sigma \propto\ln(W)$$
Where $\sigma$ is the ...
