
#109
Feb2811, 08:30 AM

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PF Gold
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#110
Feb2811, 09:07 AM

P: 2,799

You can see a THEORY as a descriptive model, or, as an INTERACTION TOOL in an inference perspective. A descriptive model is falsified or corroborated. Corroborated theories lives on. Falsified theories drop dead, leaving no clue as to how to improve. An interaction tool for inference is different, it either adapts and learns, or it doesn't. Here the falsification corresponds to "failure to learn". The hosting inference system will be outcompeted by more clever competitor. This may be one reason to suspect that the laws of physics, we actually find in nature, does have inferencial status. It's much more than playing dice. /Fredrik 



#111
Feb2811, 09:15 AM

P: 2,799

To think that we can DESCRIBE the future, is IMHO a very irrational illusion.
All we have, are expectations of the future, based on the present (including present records of the past), and based upon this we have to throw our dice. There is no other way. In this respect, the second law is one of the few "laws" that are cast in a proper inferencial form as is. As anyone seriously suggest you say; understand newtons law of gravity, but do not understand the second law? If one of them is mysterious I can't see how it's the second law. /Fredrik 



#112
Feb2811, 10:04 AM

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PF Gold
P: 1,942

Nevertheless, it is often easier to predict the future than the past. The past of a stirred fluid coming slowly to rest is far more unpredictable than the final rest state. 



#113
Feb2811, 11:36 AM

P: 1,235

The thermodynamic dimension of entropy is purely conventional. The factor is there as a connection between a measure of disorder and a measure of energy. Nevertheless, disorder can be defined without any relation to energy. The historical path to entropy doesn't imply that entropy requires any concept of thermodynamics. The widespread use of entropy today has clearly shown that it is not a thermodynamic concept. We know also that entropy finds a wide range of application in thermodynamics. It should be no surprise that the use of entropy in thermodynamics requires a conversion factor. This factor converts a measure of disorder to the width of a Maxwellian distribution. 



#114
Feb2811, 12:03 PM

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P: 5,468

http://rmp.aps.org/abstract/RMP/v64/i1/p321_1 http://pra.aps.org/abstract/PRA/v42/i4/p2467_1 http://pra.aps.org/abstract/PRA/v38/i1/p364_1 it's not a simple question to answer. 



#115
Feb2811, 01:42 PM

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P: 5,468

Even so, that only holds for equilibrium: thermostatics or thermokinetics. It does not hold in the fully nonequilibrium case. Jou, CasasVazquez, and Lebon's "Externded Irreversible Thermodynamics" and Truesdell's "Rational Thermodynamics" both have godd discussions about this. 



#116
Feb2811, 02:32 PM

P: 1,235

There need not be an answer. 



#117
Feb2811, 03:09 PM

P: 1,235

Obviously, this is again an example taken from (statistical) mechanics. Therefore, the entropy that one might consider here is again related to the distribution of energy. And therefore this one more energyrelated entropy. If we consider that any information, in the end, needs a physical substrate to be stored, then effectively the whole world is mechanical and , in the end, any entropy could be related to an energy distribution. As long as there are no degenerate states, of course ... So the question about entropy and energy could be translated in: How much information is stored in degenerate states compared to how much is stored on energy levels? (in our universe) My guess goes for no degeneracy. Meaning that history of physics was right on the point since Boltzman: it would make sense to give energy dimensions to entropy! 



#118
Feb2811, 08:19 PM

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P: 5,468

How about this example laser light. Even though laser light has an exceedingly welldefined energy, it has *no* temperature: http://arxiv.org/abs/condmat/0209043 They specifically address the difficulty in assigning a temperature and an entropy to an outofequilibrium system: "Out of equilibrium, the entropy S lacks a clear functional dependence on the total energy E, and the deﬁnition of T becomes ambiguous." Again, laser light is a highly coherent state, is resistant to thermalization in spite of interacting with the environment, has a well defined energy and momentum, and yet has no clear entropy or temperature. 



#119
Mar111, 03:40 AM

P: 1,235

It is clear that entropy is not a function of energy in general. Just consider the supperposition of two bellshape distribution. What is the "temperature" of this distribution? Even when the two distributions are Maxwellians, you would still be forced to describe the global distribution by three numbers: two temperatures and the % of each distribution in the total. This is a very common situation. Very often there are several populations that do not thermalize even when reaching a steady state (open system). For example the electron and ion temperatures are generally very different in a tokamak. Even different ion species might have different distributions in a tokamak, specially heavy ions with respect to light ions. There might even be two populations of electrons, not to mention even runaway electrons in extreme situations. In quite clear that in all these non equilibrium situations, the entropy is perfectly defined as well as the energy, but the entropy is not a function of energy anymore. Therefore, temperature cannot be defined. I will read the paper later. However, the introduction suggests that temperature could be sometimes defined in nonequilibrium situations. I agree with that with the temporary naive idea that this will be the case when at least approximately S=S(E) . One can easily built articial examples. For example, on could constrain a distribution to be Lorentzian instead of Maxwellian, or any suitable oneparameter distribution. Within this constraint S would be a function of E via the one parameter defining this distribution. Temperature should be defined in this situation. I am curious to see a more physical example in the paper. I am also curious to think about which "thermodynamic relations" would still hold and which should be removed, if any. Thanks for the reference, Michel 



#120
Mar111, 07:23 AM

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PF Gold
P: 1,942

A more detailed level is the kinetic level, characterized by microlocal equilibrium (in phase space). On this level, dynamics is governed by kinetic equations, variants of the Boltzmann equation. Entropy still exists, being defined even on the more detailed quantum level. Temperature does not exist on this level, but appears as an implicit parameter field in the hydrodynamic limit: The kinetic dynamics is approximated in a local equilibrium setting, by assuming that the local momentum distribution is Maxwellian. The temperature is a parameter in the Gaussian local momentum distribution, and makes no sense outside the Gaussian approximation. 



#121
Mar111, 09:10 AM

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P: 5,468

It's possible to recover cleanly defined thermodynamic properties in a nonequilibrium system in certain restricted cases: when the density matrix is block diagonal (if that's the correct term), for example. Conceptually, this is similar to coarsegraining or embedding a dissipative system in a higherdimensional conservative system. This only works for linear approximations the memory of a system is very short (the relaxation time is short), or the Onsager reciprocal relations can be used. As a more abstract example; we (our bodies) exist in a highly nonequilibrium state: the intracellular concentration of ATP is 10^10 times higher than equilibrium (Nicholls and Ferguson, "Bioenergetics"), which means the system can't be linearized and the above approximation scheme fails. How to assign a temperature? Clearly, there does not have to be a relationship between the "temperature" defined in terms of the distribution function of ATP and 98.6 F. 



#122
Mar111, 09:13 AM

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#123
Mar111, 10:10 AM

Sci Advisor
PF Gold
P: 1,942

By the way, not mathematicians but scientists called physicists take c=1 and hbar=1 when they discuss quantum field theory. And they actually express temperature (and distance) in terms of inverse energy, not in Meter or Kelvin. Translating to more traditional units is a triviality that can be done (and is done where needed) at the very end. 



#124
Mar111, 01:09 PM

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P: 5,468

Models can be simplified to better suit our limited understanding, at the cost of decreased fidelity to the phenomenon under investigation. 



#125
Mar111, 03:09 PM

PF Gold
P: 4,212

My advisor (a physicist) always suggests for me to use natural units since it's just the general behavior were studying (it's a more theoretical treatment)
I'm not emotionally comfortable with that, but it makes sense for a journal like Chaos. It's an exploratory science, not experimental, more theoretical = more mathematical. I see a spectrum, not a yesno situation, but then I'm a dynamicist. My work often involves turning the step function into a hyperbolic tangent. 



#126
Mar111, 03:17 PM

Sci Advisor
PF Gold
P: 1,942

Angles in degrees and temperature in degrees are both historical accidents. An extraterrestrial civilization will not have the same units  but their natural units will be the same. 


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