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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Activation energy and entropy

First assertion If a system is already in a high temperature, adding energy, will increment the entropy in a low amount (compared with a system in a lower temperature). Question (if assertion is ...
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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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Does the Higgs Mechanism contradict Entropic Gravity?

Does the Higgs Mechanism contradict Entropic Gravity? It seems like it probably does. But then again, one is a microscopic theory and the other is macroscopic. Can they live together in harmony? or ...
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Motivation for maximum Renyi/Tsallis entropy

The Conditional limit theorem of Van Campenhout and Cover gives a physical reason for maximizing (Shannon) entropy. Nowadays, in statistical mechanics, people talk about maximum Renyi/Tsallis entropy ...
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Energy formula for separating $O_2$ from mixture of $O_2$, $NH_3$ and $H_2O$

I have a physics problem I'd like to make sure I get correct. The practical aspect of this problem is that the photosynthetic efficiency of algae is inhibited with dissolved O2 in the growth medium, ...
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Does entropy measure extractable work?

Entropy has two definitions, which come from two different branches of science: thermodynamics and information theory. Yet, they both are thought to agree. Is it true? Entropy, as seen from ...
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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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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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Ignorance in statistical mechanics

Consider this penny on my desc. It is a particular piece of metal, well described by statistical mechanics, which assigns to it a state, namely the density matrix $\rho_0=\frac{1}{Z}e^{-\beta H}$ ...
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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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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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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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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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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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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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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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490 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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156 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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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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321 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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Do magnets lose their magnetism?

I recently bought some buckyballs, considered to be the world's best selling desk toy. Essentially, they are little, spherical magnets that can form interesting shapes when a bunch of them are used ...
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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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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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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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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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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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188 views

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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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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319 views

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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Did really everything begin with a state with very low entropy?

As emphasized by Penrose many years ago, cosmology can only make sense if the world started in a state of exceptionally low entropy. The low entropy starting point is the ultimate reason that the ...
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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 ...
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Statistical interpretation of Entropy

I'm preparing my statistical physics course, and while writing the lecture notes it says that a system with non distinguishable particles has much less microstates asociated with a particular ...
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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 supplied ...
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Are information conservation and energy conservation related?

as evident from the title, are both, conservation of energy and conservation of information two sides of the same coin?? Is there something more to the hypothesis of hawking's radiation other than ...
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Entropy change in a cycle with two isochoric and two adiabatic processes [closed]

Prove that the change of Entropy in a cycle with two isochoric and two adiabatic processes is 0. How can I prove that? Thanks!
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What meaning do changes in the absolute value of Gibbs free energy have in a simple expansion process?

Below is a simple representation of the thermodynamics of a steam turbine. Stream kinetic and potential energy changes are neglected and no other type of non-PV work is done besides shaft work. ...
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How long will my fridge magnet stay attached to my fridge?

I have a 500 gram neodymium magnet. It is stuck to my fridge. With the constant pull of gravity trying to pull it off how long would it stay attached to fridge? For arguments sake lets say my fridge ...
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Joining the definitions of entropy

$\int \frac{Q_{rev}}{T} = \Delta(k_B\ln\Omega)=\Delta S$ Could anyone give some definite proof for this? I was able to prove that the two definitions of change in entropy are equivalent for an ...
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Deriving an Expression for Entropy

How to derive an expression for entropy in form of $S = \ln \Omega$ from the form $\displaystyle{S = - \sum_i \; p_i \ln p_i}$ ? That is the last formula taken as a definition of entropy. Just a ...
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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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How to choose the right units to compute the phase space volume in classical statistical mechanics?

Without the natural unit $\hbar$, why doesn't it seem to be a problem for Statistical Physics to define $$S=k_B\ log(\Omega)\ ?$$ If $\Omega$ is given in one unit system and I switch to other units ...
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Nonextensive statistical mechanics

I know that the Tsallis($S_q$) entropy is called nonextensive information measure in the sense that if $P$ and $Q$ are two probability distributions then $S_q(P\times ...
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How is thermodynamic entropy defined? What is its relationship to information entropy?

I read that thermodynamic entropy is a measure of the number of microenergy states. What is the derivation for $S=k\log N$, where $k$ is Boltzmann constant, $N$ number of microenergy states. How is ...
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Simple question about a gas in a box with a moving wall

David Albert is a philosopher of Science at Columbia. His book "Time and Chance" includes this example (p 36). A gas is confined on one side of a box with a removable wall. "Draw the wall out, ...