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juanrga
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An interesting review of usual claims done in black hole literature by an expert in thermodynamics.
juanrga said:An interesting review of usual claims done in black hole literature by an expert in thermodynamics.
http://en.wikipedia.org/wiki/Black_hole_thermodynamicsAlthough Hawking's calculations gave further thermodynamic evidence for black hole entropy, until 1995 no one was able to make a controlled calculation of black hole entropy based on statistical mechanics, which associates entropy with a large number of microstates. In fact, so called "no hair"[7] theorems appeared to suggest that black holes could have only a single microstate. The situation changed in 1995 when Andrew Strominger and Cumrun Vafa calculated the right Bekenstein-Hawking entropy of a supersymmetric black hole in string theory, using methods based on D-branes. Their calculation was followed by many similar computations of entropy of large classes of other extremal and near-extremal black holes, and the result always agreed with the Bekenstein-Hawking formula.
pervect said:http://adsabs.harvard.edu/abs/1980PhLA...78..219L "Entropies need not to be concave"
seems to be in some disagreement about one of the major premises of the author. I stumbled over this while trying to see if the original paper was peer reviewed - I see other peer reviewed papers by the author, but I haven't found that the arxiv paper was ever published. Unfortunately the published papers mostly seem to require subscriptions to access.
pervect said:http://adsabs.harvard.edu/abs/1980PhLA...78..219L "Entropies need not to be concave"
seems to be in some disagreement about one of the major premises of the author. I stumbled over this while trying to see if the original paper was peer reviewed - I see other peer reviewed papers by the author, but I haven't found that the arxiv paper was ever published. Unfortunately the published papers mostly seem to require subscriptions to access.
PAllen said:I also noticed that only a few of the early paper by this author were peer reviewed, but not this one. "Expert on Thermodynamics" seems a little overblown relative to the published history. But I didn't want to bring this up until I had tried to digest the paper for its content.
For his work on irreversible thermodynamics and contributions to many areas of physics including that of Brownian motion, and in the establishment of the statistical basis of thermodynamics, and his contributions in astrophysics/cosmology.
juanrga said:Well, he is a well-known expert in thermodynamics, their works are cited by other thermodynamicians and his book in thermodynamics of irreversible processes is published by Dover classics.
twofish-quant said:The paper seems to be gooble-gook. C_p is a derivative and can be be negative or non-existent. He does a lot of equations based on the behavior of classical ideal monatomic gases, which I suppose merely shows that black holes are not made of classical ideal monatomic gasses.
twofish-quant said:And I've known extremely brilliant people in one field that were cranks when they were in another one. Roger Penrose is an example. One thing about the author is that he seems to have no experience dealing with objects in which the gravity field makes a considerable contribution to the system, which is not good when you are dealing with black holes. He seems to miss completely the point about polytropes.
He might be brilliant in thermodynamics in other fields, but the arguments that he is giving in that paper seems to be total non-sense.
I may not be an "expert in thermodynamics" but I do know a thing or two about collapsed systems. His arguments make absolutely no sense because in any sort of stellar object, you are moving energy back and forth between the material object and the gravity field, and you can't just take an object and consider only the themodynamic energy. If you want to do your bookkeepping right, you have to consider the energy that is in the gravity field, which he doesn't do.
Since he isn't including the energy in the gravity field, all of his other arguments fall apart. If you include gravity, you get the results in the first section, which he doesn't seem to understand.
juanrga said:C_p is not a mere derivative, but a physical quantity with determined properties. Your 'argument' could be re-used to say that (4) "is a derivative and can be be negative or non-existent", but it is difficult to believe someone would accept negative mass for a black hole or imaginary speed of light or nonsense as that...
Effectively, nowhere he says or even suggests that black holes are made of "classical ideal monoatomic gasses". He uses the simple case of an ideal gas for illustrating the difference between c and C.
jambaugh said:I note in the paper he also invokes a strong form of the 3rd law, [itex]\lim_{T\to 0}S = 0[/itex]. This form ignores residual entropy due to a degenerate ground state. He is here ignoring degeneracy.
His reasoning may be implicitly the "no hair" theorem but that doesn't apply. The very debate, whether BH's evaporate, is a question of observing "internal" degrees of freedom in the configurations of emitted thermal radiation (here "internal" to the surface configuration?).
Reading the short paper, he is invoking analogue physical systems (partitioned volumes, ideal gasses) without any direct thought experiments about a BH per se. I don't see the paper pointing out any physical contradictions, only the exceptional behavior of BH thermodynamics.
twofish-quant said:You add energy, the gravitational field rearranges itself and you get a different temperature. C is a quantity that includes both the effects of gravity and the physical characteristics of the object.
twofish-quant said:And in the current situation "c" is irrelevant. What matters is C.
twofish-quant said:And in the case of black holes the physical material gets crushed to a singularity in a finite time leaving behind only the gravitational field whose thermodynamic properties are not constrained by the limits that constrain physical objects. Black holes are dominated by the gravitational field so if you add energy, the field will reconfigure itself, and that's what you are observe.
The problem is that the author is used to laboratory thermodynamics in which you don't have to worry about the energy of the gravitational field, which works very badly when you figure out the thermodynamics of objects which are dominated by gravity. So in doing the energy calculations, he is completely ignoring gravity, which results in conclusions that are ridiculous.
juanrga said:If you confound internal energy with rest energy or with some other kind of energy then C can contain everything you want, but then better calls it X.
But as the author emphasizes C is not c. The non-numbered equation before (6) implies dE=CdT, but that is different from (7). Many people believes that C is the heat capacity, but for an open system dE ≠ dQ.
Not only it seems that you have not studied enough thermo, but you did not even read #12, where such claims were corrected.
juanrga said:It is evident that this kind or argument can be inverted. People as Hawking, experienced in black holes and general relativity, can say nonsense when entering in the field of thermodynamics.
Even if we ignore now that «the energy that is in the gravity field» is not well-defined in general relativity, what you say about thermodynamic energy and gravitation seems to be without any basis.
Already many ordinary textbooks explain how gravitational energy [itex]M\phi[/itex] contributes to thermodynamic energy. Of course, in a BH the situation is more complex and [itex]M\phi[/itex] is not enough, but thermodynamics in presence of gravitation continues to hold and I fail to see your point.
twofish-quant said:I've been trying to think of a "thought experiment" that illustrates what happens so that we can argue about actual science rather than personalities.
Here's an attempt...
You have a satellite that is in orbit around the Earth in a distant orbit. Because it is in a distant orbit, it orbits slowly. Now you take energy away from the satellite. What happens to it? Well, because the satellite has less energy, it's going to start falling into earth. Once it gets to a lower orbit, it's going to orbit faster.
Now imagine a cloud of atomic sized satellites in orbit around the earth. You take energy away from them. They'll drop to lower orbits. Once they drop to lower orbits, they will move faster. If you measure the temperature of the cloud, you'll find that it has increased because faster atoms = higher temperature.
So if you have a self-gravitating object, pumping energy into the object will boost things into higher orbits which slows things down and makes things cooler. Taking energy out will put things into lower orbits which speeds things up and make things hotter. In other words the object has negative heat capacity.
What's wrong with this picture? (My answer is that nothing is wrong with this picture and this is exactly what happens).
twofish-quant said:Also, a non-radiating star or black hole is a closed system.
PAllen said:Of interest to discussion of entropy of self gravitating systems is the following essay. Of particular interest is the discussion of gravothermal catastrophe - that self gravitating systems really have no equilibrium point short of a black hole.
This essay is not relevant to the core question of the validity of Bekenstein-Hawking entropy. It takes that as a given, and argues that this is exceptional and not some natural limit of ordinary gravitational collapse processes.
http://philsci-archive.pitt.edu/4744/1/gravent_archive.pdf
twofish-quant said:I've been trying to think of a "thought experiment" that illustrates what happens so that we can argue about actual science rather than personalities.
Here's an attempt...
You have a satellite that is in orbit around the Earth in a distant orbit. Because it is in a distant orbit, it orbits slowly. Now you take energy away from the satellite. What happens to it? Well, because the satellite has less energy, it's going to start falling into earth. Once it gets to a lower orbit, it's going to orbit faster.
[...]
juanrga said:The entropy of gas ideal is function of its internal energy Eint.
Its equation 5 reads E=K+U, but the thermodynamic expression in presence of fields is E=U+K+Eint.
PAllen said:In the context of discussion in that section, internal energy is held constant and can be ignored. For that section the author is explicitly treating the gas particles has incapable of changes of state. Later sections broaden that to discuss fusion and other process that do change internal energy.
For example, just a few lines before the equation you criticize is:
"Consider an ideal, uniform gas of
total energy E and kinetic energy K, containing N particles whose internal
degrees of freedom I will assume to be either nonexistent or irrelevant at the
system’s current temperatures,"
juanrga said:Reading again stuff that was corrected before is one thing, but your claim that a black hole is a closed system is too nonsensical to continue.
juanrga said:If I take away kinetic energy dK<0 (example via decelerating the satellite), but maintain constant its internal energy (U), satellite will start falling into Earth... but this have nothing to see with thermodynamics or with negative heat capacities (indeed in this case Q=0).
twofish-quant said:It has *everything* to do with thermodynamics and negative heat capacities.
twofish-quant said:Once you have enough satellites, it becomes a gas, and once you have a gas, you can do thermodynamics on it. The system of Earth and satellites is a closed thermodynamic system and you can define temperatures and heat capacities.
juanrga said:If internal energy U of the satellite is held constant and only the mechanical energy (K+V) is varied, then you do not need thermodynamics, but only mechanics. Indeed, the laws of mechanics alone explains, perfectly, why the satteliite modifies its orbit and falles when you take away kinetic energy.
Taking an enough collection of satellites does not magically convert a mechanical problem into a thermodynamic one.
Moreover, even assuming that the system of satellites can be considered a thermodynamic system, still there is none need to confound internal energy U with total energy E (including potential energy due to Earth) as done in previous posts. Similar remarks about stars.
[tex]\frac{\partial u}{\partial t} = c_V \frac{\partial T}{\partial t} + (u_k + \tau_k \psi) \frac{\partial n_k}{\partial t}[/tex]
the heat capacity is the same, as is well-known.
Of course if you want to confound rest energy with internal energy U and with total energy E, if you pretend that a black hole is a closed thermodynamic system, etc. then you can obtain anything that you want.
Of course if you want to confound rest energy with internal energy U and with total energy E, if you pretend that a black hole is a closed thermodynamic system, etc. then you can obtain anything that you want.
twofish-quant said:OK. Suppose the satellite is a hydrogen atom, and you are trying to calculate the properties of a large number of "satellites". At this point, the kinetic energy of the satellites *becomes* the internal energy of gas of satellites.
twofish-quant said:There are several other ways of calculating this. You can use the virial theorem or the equipartition theorem. See
http://en.wikipedia.org/wiki/Equipartition_theorem
http://en.wikipedia.org/wiki/Virial_theorem
In mechanics, the virial theorem provides a general equation relating the average over time of the total kinetic energy, [itex]\left\langle T \right\rangle[/itex], of a stable system consisting of N particles, bound by potential forces, with that of the total potential energy, [itex]\left\langle V_\text{TOT} \right\rangle[/itex], where angle brackets represent the average over time of the enclosed quantity.
twofish-quant said:Yes it does. You change those satellites into atoms and then have several gazillion of them. At which point you have a gas.
twofish-quant said:Except that you don't. You have the internal energy of the gas which consists of the kinetic energy of the gas molecules (H), and then the potential energy of the gravitational field (U). The relationship between the two are defined by the equipartition theorem and the virial theorem. Because the sign of the potential energy is negative, what happens is that as you remove total energy from the system, the kinetic/internal energy of the gas increases. (It's annoying here, because we are running out of letters.)
twofish-quant said:You are missing a term. The problem is that the field is not an external field but the result of self-interactions. What that means is that you have an extra \partial (\tau_k) / \partial t term which includes how the gravitational potential changes in response to external interactions.
This is off the top of my head so don't shoot me if there is a problem (and I'm getting confused with all of the letters meaning different things), but if you add energy into a gravitationally bound system then the \partial (\tau_k) / \partial t is going to be strongly positive which means that once you add that term then c_V is going to turn negative.
I'm not surprised that someone that isn't familiar with stars would make that mistake, since in laboratory experiments interacting with the system doesn't change the potential, but in self-gravitating systems, it does.
twofish-quant said:One other wrinkle is that hydrodynamics beats thermodynamics. A star takes a few minutes to reach hydrodynamic equilibrium, but several thousand years to reach thermodynamic equilibrium. Because of these time scale differences, the hydrodynamics drives the thermodynamics. What that means is that if you add energy to the system, the hydro will cause the change to happen immediately that create temperature gradients that cause the system to go out of general thermodynamic equilibrium.
So you start with an isothermal gas, and add energy to it. Rather than staying in thermodynamic equilibrium, the energy will get distributed hydrodynamically, which will throw the system out of thermo equilibrium.
twofish-quant said:No confusion. You have total energy which consists of internal energy + potential energy. Internal energy consists of kinetic energy of the gas molecules + internal degrees of freedom. Equipartition and virial theorems give you very simple relationships between these quantities. So once you have figured out the total energy, the virial theorem gives you the relationship between that and the internal energy and the potential energies.
juanrga said:No. If I assume that atoms can be treated classically as point-like particles then the thermodynamic internal energy of the gas of atoms is not the kinetic energy of the gas. The thermodynamic internal energy of a gas is defined as the total energy minus the average macroscopic kinetic energy.
But thermodynamics --which is not mechanics-- deals with internal energy, which is neither total kinetic energy nor total potential energy.
Thermodynamics is usually interested in U: internal energy. Indeed, thermodynamic textbooks contains a chapter introducing the concept of internal energy and its main properties.
Of course the value of the heat capacity [itex]c_V[/itex] is the same, because in the first case one takes partial derivative of internal energy u at constant composition and, in the second case, one takes the partial derivative of [itex]\tilde{u}[/itex] but maintaining also constant [itex]\psi[/itex] evidently.
It seems you are confused about what thermodynamics really is and does.
The total energy E of a gas is E = K + V + U, with K the total kinetic energy, V the total potential energy and U the internal energy. The virial theorem of mechanics (read the wikipedia link that you give) applies to K and V (unsurprisingly K+V is named the mechanical energy). The virial theorem does not apply to U.
If you insist on confounding thermodynamic quantities with mechanical quantities then you can obtain any bizarre result that you want even dS<0.
twofish-quant said:Except that the kinetic energy in this situation is microscopic.