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Short quick answer: From Wikipedia Entropy In thermodynamics, entropy (usual symbol S) is a measure of the number of specific ways in which athermodynamic system may be arranged, commonly understood as a measure of disorder. According to the second law of thermodynamics the entropy of an isolated system never decreases; such a system will spontaneously ...


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If all of physics is reversible like some say, then the the increasing entropy of the Universe is causing us to burn fossil fuels as much as we are increasing the entropy.


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If you correct plank units by using Einstein's Appendix 2 of "Relativity" relation meters = i c seconds, and carry the i through all equations, converting any seconds units to meters, you get better insight. For example, this gives E= -mc^2 instead of E=mc^2, which cosmology agrees with. So you also convert all mass units to negative energy units. You then ...


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The answers seem too scattered, abstract, and complex. It is important to keep in mind temperature is a direct measure of the average (or RMS) kinetic energy of the particles. First let's be clear and say each container contains the same number of particles in the same size volume. Let their temperature be different by a factor of two. If you add enough heat ...


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I like to think if it as connected to potential in the way described below, but transmitting or otherwise erasing it might be called kinetic energy. The one thing for sure is that there is a minimal entropy generated when a bit is erased. Landauer's principle says at least kT ln(2) energy must be lost as heat when a bit is erased. At least k ln(2) entropy ...


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Antimatter is matter going backwards through time. No it isn't. Whilst that idea might appear to have some pedigree, (see retrocausality on Wikipedia), it's bunk I'm afraid. Antimatter is like matter, but it has the opposite chirality. Google on positron chirality. Whilst one can mathematically model the positron as a "time reversed electron", it isn't ...


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Antimatter increase in entropy over time. We can verify this with a thought experiment. Take ten positrons. Put five in one side of a chamber with a barrier and then the other 5 on the other side of the barrier in the same chamber. The chamber and barrier are also made of antimatter. The positrons repel each other and so each have a certain amount of kinetic ...


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I just want to add to Lumo's answer: The paper by vafa and Strominger instigated a lot of work in determining the statistical formulation of entropy in black holes. Although it must be pointed out that most of these are for cases with supersymmtry and (near) extremal conditions at small couplings. There has also been work in trying to address the microscopic ...


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This is a very profound question in physics. Given that a black hole has an entropy which scales as $$S_{BH} \sim \frac{A}{4}, $$ the question is how does this relate to $S_{Boltzmann} = K_B \ln W$. As in, what are the microstates of the theory which hold the information in the black hole. This was answered in part by a series of papers by Vafa, Strominger, ...


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Here is how to see this answer: In the standard model of cosmology, which is given by the FLRW (Friedmann-Lemaitre-Robertson-Walker) solutions of Einstein's field equations, symmetries of isotropy and spatial homogeneity require that such universes be perfect fluid universes. As you know from thermodynamics, perfect fluids have their entropy conserved! So, ...


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The entropy of a black hole is proportional to its surface area. If the Universe follows the same rule, then as it expands entropy increases, but entropy per volume might be constant, or even decrease. For example, if life continues to increase in its ability to efficiently use Gibbs free energy from Sun photons, fossil fuels, and nuclear sources, it might ...


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I) If there are boundaries, how can we know about what happens there with entropy? The preferred way to think of the universe today is that it does not have any boundaries. But there is no way to be sure unless we find such a boundary. If our universe was enclosed inside a perfectly rigid hull impenetrable to everything including gravity (infinite ...


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For an infinitesimal heat transfer $\delta Q$ the inequality of Clausius states that $\Delta S = S_1-S_0 = \int_0^1 {\dfrac {\delta Q_\text{rev}}{T}} > \int_0^1 {\dfrac {\delta Q_\text{irrev}}{T}}$ Here $\delta Q_\text{rev}$ and $\delta Q_\text{irrev}$ denote reversible and irreversible heat transfers, respectively. Thus if the process is reversible ...


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In macroscopic units it should be $$S=-R\alpha \log(\alpha e^{-S_1/R})-R(1-\alpha)\log\Big(1-\alpha)e^{-S_2/R}\Big) \\=\alpha \Big(S_1-R\log\alpha\Big)+(1-\alpha)\Big(S_2-R\log(1-\alpha)\Big),$$ where $R$ is the universal gas constant. In the pure case, this reduces to the textbook formula. But such a formula cannot be true in general. The general formula ...


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Suppose you start with a system in some state $P_1, V_1, T_1$ and you add some quantity of heat $\Delta Q$ to it so the system changes to a different state $P_2, V_2, T_2$. The final state will depend on how you added the heat $\Delta Q$. Adding the heat $\Delta Q$ in a reversible process will result in different values for $P_2, V_2, T_2$ compared with ...


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Wave function collapse (or a measurement on the QM system) is not unitary since it is a projection of the state vector.


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To give you the idea of the complexity of this problem, consider that the dynamics of a single fluid is governed by the Navier-Stokes equation, which is already impractical to solve. $$\frac {\partial}{\partial t} (\rho u) + \nabla \cdot (\rho u \otimes u + p I) = \nabla \cdot \boldsymbol \tau + \rho g$$ Then this equation is coupled to probably three ...


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I only have a small comment to make on this topic. I think rather than use the word " subjective" it would be more exact to say that entropy is arbitrary, in the sense that, the value of entropy for your system depends on the variables you use to describe your macrostate, but once the choice is made, then the entropy is determined by the objective forces you ...


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You're missing a minus in the entropy definition - $S=-Tr(\rho\ln\rho)$ Entropy of a unitarily evolving system (doesn't matter in which picture) is conserved (The entropy is a trace of a function of the density matrix "operator" thus it depend solely on the eigenvalues of it's input operator, but the eigenvalues of the density matrix don't change under ...


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What Scott's saying Okay, so the basic assumption I can phrase as this: The universe is finite and has an end. During The End, cosmic inflation does not rip every particle apart into its own universe, and no cyclic model of cosmology predominates: The End of the universe is instead one big "soup" of particles in thermal equilibrium, all having some low ...


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I just want to amplify on what @Travis said and let me quote "Jaynes: Gibbs vs Boltzmann Entropies" who credits Wigner for this concept of THE "ANTHROPOMORPHIC" NATURE OF ENTROPY "...After the above insistence that any demonstration of the second law must involve the entropy as measured experimentally, it may come as a shock to realize that, nevertheless, ...


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You have a few confused ideas here- which is quite normal, because it is a confusing subject that is often not described very well. Instead of addressing them all specifically, I will answer the central question: Entropy is objective. It is true that one must specify exactly what degrees of freedom are in and out of your system to say what the entropy is. ...


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Entropy is subjective in the sense that you get to pick which macroscopic observables you care about keeping track of (usually, for instance, you care about things like temperature, pressure, etc.). Once you've defined the macroscopic observables, entropy is defined as the logarithm of the number of possible microstates that give rise to those macroscopic ...


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and with some special apparatus we notice that the gas particles themselves do not seem to be moving either. The assumptions imply the particles move with high speed. Their velocities differ less one from each other, but the particles are moving. The amount of information needed to completely specify the contents of the box is reduced, because 1) ...


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I am not sure if this answer will give you an intuitive understanding of the result, but I think it may be useful as it shows the assumptions behind it. What your result means is that in an idealized situation when the volume gas or solute occupies is shrunk slightly by $\delta << V$ while its energy remains the same (let's say, isothermal compression ...


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A quick answer is that the entropy of the universe is actually encoded in the Weyl curvature. Einstein's field equations: $R_{ab} - \frac{1}{2}g_{ab} R + \Lambda g_{ab} = \kappa T_{ab}$ contain only ten independent components of the Ricci tensor for a 4-D spacetime. However, this is obtained from a contraction of the Riemann curvature tensor, which itself ...


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Really how does the entropy of the universe increase? The statement "entropy of the universe increases" is a misconception about thermodynamics. The problem with that statement, as CuriousOne has written in the comments, is that universe is not a closed system amenable to thermodynamic description. It has no volume, no temperature and we have no means ...


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Then how can the entropy of the universe increase? Because the universe is like your gas with no surroundings. But see the stress–energy–momentum tensor, and note that it "describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics". See the shear stress term? Space is more like a gin-clear ...


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In order to make this work, water needs to flow through the venturi, which takes energy and increases entropy. This energy by far surpasses the energy of conversion of random particle motion to orgonized motion. Thus entropy increase due to making water flow is larger than the corresponding entropy decrease due to making random particles flow in organized ...


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Noether's theorem states that if a system has a continuous symmetry, there is a quantity related to this symmetry, called the Noether charge, which is conserved. It does not state anything on the fact that adding a constant term to a measurable quantity may or may not change the physical description of the system. Only some physical quantities in fact are ...


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Lie down and fall asleep. Right on the razor's edge between awake and asleep, look at what it all looks like. See yourself and the world in unison, fading away... slowly, and at the same time instantaniously. Then, in the morning, be thankful that your experience was merely that of falling asleep, and not a more permanent heat-death. (The question is ...


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Take a piece of meat of 100Cal and almonds of 100Kal and a crystal of sugar of 100Cal. Which has the lower entropy at the same temperature? Certainly the crystal, because it is the most ordered. Then in ordering come the almonds , which has a simpler composition of molecules and higher density. Meat has blood, mitochondria, cells, nuclei of cells . This ...


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The route of finding $\frac{\partial S}{\partial x}$ and $\frac{\partial S}{\partial T}$ is the more practical route. $\frac{\partial S}{\partial x}$ can be found using a simple Maxwell relation for the Helmholtz free energy: $$dA=dU-d(TS)=Jdx-SdT$$ $$\left. \frac{\partial A}{\partial x}\right|_T = J \, \, \mathrm{and} \, \, \left. \frac{\partial A}{\partial ...


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This would depend on what entropy of plant and animal is supposed to mean. Originally, entropy describes systems in states of thermodynamic equilibrium. If you want to introduce similar quantity for systems in more complicated states, (plant or animal are not systems in thermodynamic equilibrium), you need to give its definition. There is no universally ...


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Boltzmann's formula for entropy is S = k * log W, where S is entropy, k is a constant, and W is the total number of ways the micro particles of a system can be re-arranged without altering the macro appearance and properties of the system. What Boltzmann had in mind was a gas tending toward thermodynamic equilibrium. For any other system, the measurement ...


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I think you have a fundamental misunderstanding of what the heat death really is. Any observer, whether they are a time traveler, observer from another universe, or whatever, would just see a lot of empty space. The first thing to know is that the heat death is not a single event. The universe, after heat death, is dead in the sense that nothing is ...


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I would say it looks like nothing. The heat death requires that the whole universe is thermodynamically homogeneous, and that the universe has reached its maximum entropy. This means that every thing becomes a disordered lump of very sparse matter, without anything to see whatsoever. It's as if the universe is in a state akin to the "chaotic nothingness" ...


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From a thermodynamical point of view, living beings are able to reduce their entropy by exporting entropy to the external world. This does not contradict the 2nd principle, since living beings are open systems. For this reason, in a thermodynamically homogeneous universe (heat death), no change in the entropy can occur, and consequently no living beings (nor ...


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I am sorry for the joke about consciousness. Jokes sometimes lower entropy; apparently did not succeed this time. There is indeed a lot of confusion related to the second law. The "proof" of Jaynes as many others have additional assumptions that seem innocuous. They are not. The best is to depart from too general theorems, since in difference to math. in ...


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The answer to the question you are trying to ask is yes, but I will need to do a bit of explanation. First, be aware the entropy is like mass or volume, in the sense that if you have two copies of something, the two copies will have twice as much entropy as the single object, exactly the same way they have twice the mass or volume. Because of this, you ...


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As Joannes says, the two principles belong to two different theories: the least action principle is a principle about the (conservative) laws of motion and a proposition about the paths actually followed by the degrees of freedom of mechanical bodies the maximum entropy principle refers either to thermodynamics to figure out in which direction will a ...


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Its a long time controversy. The Hamiltonian time reversible equations are as a matter of common sense not capable and incompatible with the second law. Moreover if in any system like Earth or Cosmos the growth of order is observed it means that the system is open and fed with negative entropy flux by a source of coherent momentum/energy. Moreover if the ...


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Normally $H(X|Y)$ means conditional entropy. In this case I don't think there is any generally accepted definition of Renyi counterpart. There is, however, a recent Master thesis which lists some possibilities including a new propositions by the author, which seems to be quite reasonable: http://web.math.leidenuniv.nl/scripties/MasterBerens.pdf If you ...


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TVOC 1.pdf Snell's Law.pdf Optical WedgeA.pdf http://www.raydextech.com/led-collimation.html


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Since state $\sigma$ is not in thermal equilibrium I don't think one can use your definition of "thermodynamical" entropy. In fact, one should instead use Von Neumann entropy, which is a correct measure of statistical (so not quantum!) uncertainty. There is no other "classical" or "thermodynamical" entropy in quantum systems. As you mentioned, for a thermal ...



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