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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The definition of entropy in quantum mechanics

I have seen entropy with several different definitions. Like Von Neumann entropy and Rényi entropy, etc. So I am curious why there are so many different definitions in quantum mechanics while only ...
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261 views

An explanation for the Landauer's principle

Has anyone understood the Landauer's principle? What is the current status? In specific, is there a theoretical derivation of the Landauer's Principle?(not the heuristic one based on Salizard's ...
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269 views

Do laws of thermodynamics have a place in Theory of Everything? [closed]

I am having a difficulty understanding why second law of thermodynamics is still a valid universally accepted concept. I understand it works on paper for describing isolated heat systems. However, I ...
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173 views

Minimal Maxwell's Demon

I would like to understand where the waste heat is generated in the Maxwell's demon problem. To this end I've come up with the simplest scenario I can think of. If my scenario is workable I am hoping ...
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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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827 views

Formal demonstration that minimizing the free energy equals maximizing the entropy

I never had great intuition when it came to thermodynamic concepts and potentials even though reading a textbook and completing the exercises has never been a huge problem. In one of them, I was ...
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Why does the law of increasing entropy, a law arising from statistics of many particles, underpin modern physics?

As far as I interpret it, the law of ever increasing entropy states that "a system will always move towards the most disordered state, never in the other direction". Now, I understand why it would ...
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250 views

Speed of Entropy change

If time in systems moving with different speed goes differently, does speed of entropy change differ in these systems? (is "speed of entropy change" a valid term? can we compare them?)
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394 views

Does entropy decrease through measurement?

For an electron in its rest frame, we have an entropy $$ S = \log 2, $$ which comes from the 2 possible spin directions along z-axis. If the measurement $S_z$ changes its state to $\left| + ...
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Qualitative discussion about entropy and disorder

Many discussions about entropy and disorder use examples of decks of cards, pages of books thrown in the air, two gases being mixed in a container, even the state of a nursery at the end of the day ...
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358 views

Entanglement Entropy

I needed some references which involves, the basic definition and motivation for Entanglement Entropy, and its one or two applications to many-body physics/black holes.
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Why do reversible processes not increase the entropy of the universe infinitesimally?

The book Commonly Asked Questions in Thermodynamics states: When we refer to the passage of the system through a sequence of internal equilibrium states without the establishment of equilibrium ...
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231 views

Information Loss in annihilation

The concept of information loss is usually discussed with respect to a black hole. My understanding is that whatever matter you put into the black hole, it has only 3 "hairs" and so one doesn't know, ...
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Black hole entropy

Bekenstein and Hawking derived the expression for black hole entropy as, $$ S_{BH}={c^3 A\over 4 G \hbar}. $$ We know from the hindsight that entropy has statistical interpretation. It is a measure ...
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Zero entropy change

If you put a object in contact with a heat reservoir that is infinitesimally higher in temperature than the object and allow equilibrium to be reached the entropy change is zero right?
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Was the Universe's entropy equal to zero at the Big Bang? Is zero-entropy state unique?

It is postulated by many cosmologists that at the Big Bang time the universe was in an unusual low entropy state. Does this claim specifically mean that the entropy of the initial universe was zero? ...
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249 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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287 views

Fluid Dynamics - Water Bottle Drink Mix: Air or No Air?

If you take an ordinary sized plastic water bottle full of water and pour a packet of powdered (or liquid) drink mix into it, Will shaking the bottle with the cap screwed on to dissolve the mix into ...
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274 views

Entropy: two explanations for the same quantity?

I studied thermodynamics and I saw the following definition for entropy: $$ \Delta S = \int_1^2 \frac{\text{d}Q}{T} $$ that we use to calculate $\Delta S$ for different types of transformations. In ...
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How is $\frac{dQ}{T}$ measure of randomness of system?

I am studying entropy and its hard for me to catch up what exactly is entropy. Many articles and books write that entropy is the measure of randomness or disorder of the system. They say when a gas ...
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957 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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131 views

Where is the critical moment where the microcanonical ensemble enters the justification for the equilibium state?

As explained in many books, for the microscopic justification of the second law of thermodynamics (lets formulate it as the total entropy takes maximum among all possible exchanges of two systems), ...
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Kolgomorov entropy issues

I am long been confused by these entropy terms. Would be obliged if an explanation is provided in less technical jargon What are the differences between Shannon's entropy, topological entropy and ...
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428 views

Question about entropy and “smart materials” (that remember shape)

We all know that entropy is the measure of chaos in the system, and it's always increasing in the system. Now comes my question - how does entropy work in smart materials? Here is a youtube video ...
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Reference request for low entropy big bang

There is a somewhat widely accepted argument that the second law of thermodynamics exists because the universe began in a low-entropy state. I'm writing a paper that mentions this (and must be ...
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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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133 views

Can entanglement be used to decrease entropy of two systems?

I know that entanglement can create correlation between systems. Would it be true to say that entanglement create constraints between systems? Can constraints be used to lower the total entropy of ...
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What is the relationship between Energy, Entropy, and Information?

What is the relationship between Energy, Entropy, and Information? I read this - What Is Energy? Where did it come from? - and the top answer says that 'energy' is an abstract number that is a ...
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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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Does radiation change entropy?

Are there entropy changes associated with the transmission of energy from the sun to the earth? Does radiation differ from other modes of heat transfer with respect to the entropy changes? Are the ...
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295 views

Wasn't the Hawking Paradox solved by Einstein?

I just watched a BBC Horizon episode where they talked about the Hawking Paradox. They mentioned a controversy about information being lost but I couldn't get my head around this. Black hole ...
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Why is information indestructible?

I really can't understand what Leonard Susskind means when he says that information is indestructible. Is that information that is lost, through the increase of entropy really recoverable? He ...
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Area law for Entropy in Loop Quantum Gravity

In connection with the long saga of the (claimed) microscopic calculations of the Hawking-Bekenstein entropy in (3+1) Loop Quantum Gravity (LQG) and related approaches I have the following question: ...
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342 views

How is the logarithmic correction to the entropy of a non extremal black hole derived?

I`ve just read, that for non extremal black holes, there exists a logarithmic (and other) correction(s) to the well known term proportional to the area of the horizon such that $S = \frac{A}{4G} + K ...
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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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Influence of Joe Rosen work, is it marginal, or significantly accepted?

I have prepared a paper that relies on work of Joe Rosen on symmetry (e.g. "Symmetry Rules: How Science and Nature Are Founded on Symmetry"). I am wondering about his influence. For example, when I ...
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The entropy of a static granular mixture

Regarding static granular mixtures (pile of sand - particles with different sizes), is there an expression that will give me the entropy of such a mixture? I am interested in finding the entropy of ...
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Confusion regarding entropy, reference papers request

1.a In paragraph at Wikipedia/Entropy it is stated: This is because energy supplied at a high temperature (i.e. with low entropy) tends to be more useful than the same amount of energy ...
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435 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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Connection between entropy and energy

An isolated system $A$ has entropy $S_a>0$. Next, the isolation of $A$ is temporarily violated, and it has entropy reduced $$S_b ~=~ S_a - S,\space\space\space S\leq S_a.$$ Is it true to say: the ...
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86 views

System moves away from equilibrium $\rightarrow$ it has energy added?

Suppose there is an isolated system $A$ at time $(-\infty, t_1)$, whose entropy is $S=S_{max}$, i.e. it is at thermodynamical equilibrium. Between moments $[t_1, t_2)$ the isolation is violated and ...
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Reference paper to support information — energy relation ($kT \ln2 \rm\frac{J}{bit}$)

In answer to Maxwell's Demon Constant (Information-Energy equivalence) there is stated that one bit of information allows to perform $kT \cdot \ln2$ Joules of work. Which paper supports the ...
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Is a closed system receiving heat guaranteed to have entropy below maximum?

Isolated system will preserve its entropy unchanged (for fully reversible system) or it will increase its entropy (for system with irreversible processes). For a closed system, it can receive energy ...
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502 views

How did the energy/entropy/volume/pressure/temperature relationship exist at the Big Bang and how did it evolve thereafter?

According to the current Big Bang with inflation cosmological model? I was under the mistaken impression that there was very low volume, very high temperature/pressure, very low entropy and the Big ...
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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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Does the second law of thermodynamics tell me how the entropy changes?

In thermodynamics I can e.g. compute the properties of ideal gases with certain energies $U_1,U_2$ in boxes with certain volumes $V_1$ and $V_2$. Say I have two such boxes and they have some specific ...
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Does measurement, quantum in particular, always increase the total entropy?

Measurement of a quantum observable (in an appropriate, old-fashioned sense) necessarily involves coupling to a system with a macroscopically large number of degrees of freedom. Entanglement with this ...
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385 views

What's the validity of the thermodynamic definition of entropy?

Thermodynamic Entropy Variation is defined as $$\Delta S = \int_i^f \frac{dQ}{T},$$ where $i$ and $f$ are the initial and final states of the process. My question is: does this equation apply to ...
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What is a qualitative explanation for order of values of standard entropies of formation for isomers of hexane?

I have literature values for the standard enthalpy and Gibbs energy changes of formation at 298 K, $\Delta H_\text{f}^o$ and $\Delta G_\text{f}^o$, for product in the ideal gas state. Since $G=H-TS$ ...
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Is there an abstract notion of heat within a microscopical system?

The microstates of a system are said to be unobservable. I can introduce the entropy as a measure of the number of microstates, which lead to the same macroscopic variables. So in this detailed ...