A important property of all systems in thermodynamics and statistical mechanics. Entropy characterizes the degree to which the energy of the system is *not* available to do useful work
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Definition of entropy
In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) entropy of a variable $X$ is ...
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Entanglement and Black holes
If you have two entangled quantum states, One state falls into a black hole and you measure the other state, What can you say about the state that has fallen into the black hole?
If you have billions ...
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1answer
216 views
How much energy Maxwell's demon will earn?
Suppose we have one mole of one-atom ideal gas at temperature $T$.
Suppose Maxwell's daemon has separated molecules into two sections, one with speed below mean and another with speed above mean.
...
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53 views
The most general entropy
What is the most general (likely non-extensive) entropy allowed/realized in Nature and its symmetry group of transformations?
We know Shannon-Gibbs-Von Neumann entropy, Tsallis entropy, ...
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3answers
414 views
Does high entropy means low symmetry?
According to Bogolubov postulate (various texts name it differently) in Non-equilibrium thermodynamics, the number of needed parameters to describe our system is decreasing with time, and finally at ...
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comments on entropy and direction of time in Landau and Lifshitz stat mech
In Landau and Lifshitz's Stat Mech Volume I is the comment:
Thus in quantum mechanics there is a physical non-equivalence of the two diretions of time, and theoretically the law of increase of ...
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If particles can find themselves spontaneously arranged, isn't entropy actually decreasing?
Take a box of gas particles. At $t = 0$, the distribution of particles is homogeneous. There is a small probability that at $t = 1$, all particles go to the left side of the box. In this case, entropy ...
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5answers
1k views
Will adding heat to a material increase or decrease entropy?
Does adding heat to a material, thereby increasing electrical resistance in the material increase or decrease entropy?
Follow up questions:
Is there a situation were Heat flux ie. thermal flux, ...
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71 views
What is the entropy of a system when its volume tends to zero?
Say that a closed system has $n$ dimensions and is in the shape of a $n$-ball with a radius of 1, it's volume will be
$$\frac{\pi^\frac{n}{2}}{\Gamma(\frac{n}{2}+1)}$$
which tends to 0 yet is not ...
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1answer
96 views
Mathematical proof of non-negative change of entropy $\Delta S\geq0$
I understand that we can prove that for any process that occurs in an isolated and closed system it must hold that
$$\Delta S\geq0$$
via Clausius' theorem. My question is, how can I prove this in a ...
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625 views
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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237 views
Loschmidt's paradox - really a paradox? [duplicate]
Is Loschmidt's paradox a paradox even today?
In other words, is the paradox resolved or not?
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1answer
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Could entropy explain dark energy?
This was 3rd beer idea, so please bear with me. What if the universe was not actually expanding but the speed of light was slowing? Wouldn't that be indistinguishable to our observations? Either way ...
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184 views
Order = Energy = Mass?
Here is a following problem I encountered when chatting about physics with my friend:
Let us imagine a classical example of ordered state of matter in thermodynamic sense: let's take a cylinder ...
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0answers
29 views
Calculating the change in entropy in a melting process
I have a homework question that I'm completely stumped on and need help solving it.
I have a $50\, \mathrm{g}$ ice cube at $-15\, \mathrm{C}$ that is in a container of $200\, \mathrm{g}$ of water at ...
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1answer
47 views
Negative temperature and Absolute hot
This video explains that heat at negative temperatures flows from the negative object to the normal object. If the temperature of the normal object is absolute hot, what happens with the heat? The ...
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1answer
47 views
Would the universe get consumed by blackholes because of entropy?
Since the total entropy of the universe is increasing because of spontaneous processes, black holes form because of entropy (correct me if I'm wrong), and the universe is always expanding, would the ...
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1answer
229 views
Relation between external magnetic field intensity H, magnetisation M and the entropy?
How are the external magnetic field intensity H, magnetisation M and the entropy related to each other? i.e. if I change the magnetic field intensity by dH what will be the change in entropy dS in ...
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168 views
Simplifying the explanation of a low-entropy Big Bang
The claim that the young universe was in a low-entropy state seems at odds with
maximal entropy being thermal equilibrium, and
the young universe being in thermal equilibrium.
I've looked at some ...
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3answers
131 views
Integrating factor $1/T$ in 2nd Law of Thermodynamics
How would you prove that $1/T$ is the most suitable integrating factor to transform $\delta Q$ to an exact differential in the second law of thermodynamics:
$$dS = \frac{\delta Q}{T}$$
Where $dS$ is ...
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2answers
37 views
Decrease in entropy in a fluid flow
Let's imagine a section of a pipe through which a fluid, gas for example, flows. When there is no pressure gradient, there is no flow. However, that does not mean that the molecules are at rest. They ...
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1answer
59 views
Amount of energy to separate Gases - relationship to concentration
I want to understand the efficiencies of separating mixed gases, and for that I want to understand the thermodynamic limit case. Looking at the wikipedia page for entropy of mixing, I find the ...
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Entropy / speed relationship in vehicle
I'm trying to figure out if the speed of a motorized vehicle (a car of instance) varies with the 'age' of the vehicle.
If we suppose a vehicle of a given 'age', considering the yield loss of the ...
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1answer
67 views
What happens at the interface between two universes with opposite thermodynamic arrows of time?
I was trying to think but cannot figure it out. For instance, if the interaction is small, for instance limited to a windows, the observers in each universe will see that the other goes in reverse. ...
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1answer
62 views
Basic energy calculation for N identical spin system
We have a system that has N identical spins $n_i$, and each spin can be in state 1 or 0. The overall energy for the system is $\epsilon\sum_{i=1}^{N}n_i$.
My understanding: There is only one ...
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2answers
538 views
About Susskind's claim “information is indestructible”
I really can't understand what Leonard Susskind means when he says that information is indestructible.
Is that information really recoverable?
He himself said that entropy is hidden information. ...
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3answers
136 views
Does entropy alter the probability of independent events?
So I have taken an introductory level quantum physics and am currently taking an introductory level probability class. Then this simple scenario came up:
Given a fair coin that has been tossed 100 ...
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1answer
72 views
Uncertainty and Thermodynamics
Dilemma
The uncertainty principle of energy and the 2nd law of thermodynamics don't add up : the uncertainty principle of energy says that
$\Delta \tau \cdot \Delta E \ge \frac{h}{4\pi} = ...
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1answer
49 views
Why does a temperature increase on a fixed volume increase entropy?
I heard that this statement is correct. However, it seems odd to me. The number of possible microstates is still the same, so isn't the entropy constant?
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2answers
183 views
Does entropy really always increase (or stay the same)?
Consider this image. If the big (grey) molecules were all to spontaneously move to the left, and the small ones were to move to the right, there would be an increase in order.
While unlikely, ...
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2answers
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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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3answers
320 views
Is there a mechanism for time symmetry breaking?
Excluding Thermodynamic's arrow of time, all mathematical descriptions of time are symmetric. We know the arrow of time is real and we know the equations describing physics are real so is there any ...
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4answers
351 views
Second Law of Thermodynamics and the Arrow of Time: Why isn't time considered fundamental?
I've come across this explanation that the "arrow of time" is a consequence of the second law of thermodynamics, which says that the entropy of an isolated system is always increasing. The argument is ...
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2answers
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Von Neumann Entropy: varying definitions
I have seen different authors define von Neumann entropy in different ways. In particular, some use the natural logarithm and others log to base 2. What is the reasoning for this? Does it make any ...
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Difficulties with understanding total entropy change and unavailabillty
Of course, I know the fact that the entropy of an isolated system never decreases. Neverthless what makes me confused about the entropy(or change of entropy) of an isolated system is the explanation ...
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Why is the equation for Entropy of an ideal gas that undergoes reversible change in T at constant Pressure like this?
Why is the equation for change in Entropy for a reversible change in $T$ at constant $P$ described as
$$\Delta S = n C_p \ln\frac{T_f}{T_i}$$
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Why isn't the Bekenstein-Hawking Entropy considered the quantum gravitational unification?
Based on the Bekenstein-Hawking Equation for Entropy, hasn't the relationship between quantum mechanics and gravity already been established.
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1answer
75 views
Is there a relation between supersymmetry and entropy?
Considering that entropy denotes the level of order/disorder in a system, would it be possible for entropy and supersymmetry to exist at the same time? Or, are they entirely unrelated?
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How to solve state parameters using these givens for an ideal gas?
In a thermodynamic turbine using air as an ideal gas, given that you have a known inlet temperature value $T_i$, a known exit pressure value $P_e$, a known inlet and exit velocity $V_i$ and $V_e$, a ...
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2answers
349 views
What is the physical or mathematical meaning of the Gibbs-Duhem equation?
The Gibbs-Duhem equation states
$$0~=~SdT-VdP+\sum(N_i d\mu_i),$$
where $\mu$ is the chemical potential. Does it have any mathematical (about intensive parameters) or physical meaning?
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What is information?
We're all familiar with basic tenants such as "information cannot be transmitted faster than light" and ideas such as information conservation in scenarios like Hawking radiation (and in general, ...
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4answers
598 views
What does third law of thermodynamics tell us?
I just have a question concerning the third law of thermodynamics.
The third law describes that the entropy should be a well defined constant if the system reaches the ground state which depends ...
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1answer
48 views
Do gasses always mix because of their Gibbs free energy?
As far as I know there are no two gasses that don't mix (excluding demixing by gravitational effects). For me, as someone working with fluids and surface tensions a lot, this means that the surface ...
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0answers
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Entropy change relation to the number of lost bits
Can we use entropy change value to define the (perhaps fractional) number of
bits of information that are lost by and, or, xor gates?
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1answer
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How can dQ/T be interpreted as a system's level of disorder?
Long before statistical mechanics, entropy was introduced as:
$dS = \frac{dQ}{T}$
At the time when entropy was introduced in this manner, was it known that entropy represents how "disordered" a ...
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6answers
224 views
Entropy and Crystal Growth
I was reading about growing single crystals and I'm a little confused about this -
In most crystal growing processes, a "seed crystal" is used, and the rest of the material crystallizes on the seed ...
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1answer
48 views
What are the units of the Bekenstein bound?
Working with the Wikipedia definition of the Bekenstein bound:
$S \leq \frac{2 \pi R k_bE}{\hbar c}$
$2\pi R \ $ is $m^2$
$k_b$ is $\frac{J}{K}$
$E$ is $J$
$\hbar$ is $J*s$
$c$ is $\frac{m}{s}$
...
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How to compute configurations (entropy) of a system?
If we have a system $X$ consisting of subsystems $X_1$ and $X_2$.
We also know that $X_1$ and $X_2$ have eigenstates $H_1 = 1 \times 10^{20}$ and $H_2 = 1 \times 10 ^{22}$.
Can we calculate the ...
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1answer
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relation between first law of thermodynamics and statistical mechanics definition of entropy
From the definition of entropy as $S= - Tr (\rho\, ln \rho)$ one obtains that
$S = \frac{\langle E \rangle}{T} + \log Z.$
The first law of thermodynamics has
$dS = {dE \over T}$.
Why is there no ...
