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Alternative definitions of energy? 
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#127
Dec611, 12:09 AM

P: 11

In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems. Since work is defined as a force acting through a distance , energy is always equivalent to the ability to exert pulls or pushes against the basic forces of nature, along a path of a certain length.
The total energy contained in an object is identified with its mass, and energy, cannot be created or destroyed. When matter is changed into energy , the mass of the system does not change through the transformation process. However, there may be mechanistic limits as to how much of the matter in an object may be changed into other types of energy and thus into work, on other systems. Energy, like mass, is a scalar physical quantity. In the International System of Units (SI), energy is measured in joules. 


#128
Dec611, 09:55 AM

P: 476

2) Moreover, notice that there is two meanings for «Classical Physics». Older meaning as «prerelativistic» and the more modern meaning as «nonquantum». 


#129
Dec611, 10:56 AM

P: 5,462

@juanrga
Your posts in this thread have taken me to an unfamiliar area and certainly set me thinking so thanks. However I would appreciate your take on my comment at the end of post#107 about energy transfer. 


#130
Dec611, 03:37 PM

P: 755

Sorry for the delay, juanrga. I'd like to continue the discussion, but in order to make our discussion more comprehensible, I'll first sketch my general ideas and get to your references and statements later.
In QM, dissipation and irreversible dynamics can be derived from the reversible Hamiltonian dynamics of a larger isolated system. This whole system consists of the system of interest and it's environment. So the dissipator of open systems can be derived from unitarian dynamics. [Taking the dynamics to be Hamiltonian is just a restriction of the initial state to be pure] In classical mechanics, this seems to be impossible. Although one could imagine something like the increase in entropy in one part of the whole system could be compensated by a decrease in another, this is certainly not true for arbitrary initial conditions. So classically, dissipation and irreversible dynamics can only be explained by neglecting correlations (HTheorem). They do not arise in a fundamental way from reversible dynamics. Quantum mechanically, they do for open systems. This fundamental difference between classical mechanics and QM leads to the question, how irreversible dynamics in isolated systems could possibly be encountered. One way is to say our current theory is not exactly right, we have to either change the formalism or the interactions. Another way is to question the isolatedness of systems with irreversible dynamics. I definitely prefer the latter. Real "isolated" systems, like a gas in a box, have borders with which they interact. The isolationidealization (sounds like a big bang theory episode title :D) is probably good enough as long as we talk about energy and particle exchange. But when it comes to correlations (especially entanglement) we have to be much more careful. If I get your references right (unfortunately I don't have access to all of them), their argument for the approach of isolated systems to equilibrium relies on taking the thermodynamical limit. Doing this is certainly useful in static (equilibrium) situations, where we don't care how we actually got into our state. In the context of dynamics, I think this is unphysical. Adding particles and increasing the box size involves interactions with the system, which have to be included in the dynamics. I think this is the crucial point in many arguments concerning "isolated" systems. 


#131
Dec711, 10:43 AM

P: 476

dU/dt = dQ/dt + dW/dt but thermodynamics alone cannot say you the rates. The rates are obtained from rate equations as Fourier law, chemical kinetics laws, diffusion laws, etc. If A and B are contiguous then energy either belong to A or to B. If the systems are not contiguous, then energy could be stored in some intermediate system C before arriving at B. 


#132
Dec711, 11:04 AM

P: 476

Most of the literature in the topic of open systems is completely wrong about the origin of irreversibility. They do not derive irreversibility but force irreversibility by mathematically invalid manipulations. Of course the final equations tested in the lab are valid, but are not compatible with unitary and time reversible equations. This limit would not be taken seriously, but only operationally. Somehow as obtaining the nonrelativistic limit through taking the limit c → ∞ would not be taken literally seriously (c is a constant!). 


#133
Dec811, 08:55 AM

P: 755

Please elaborate on why you call such dynamics reversible. We want to learn something about the dynamics of one given system. We can't just replace it with a similar system and say that the statements derived for the new system are true for the system of interest. In their framework, it seems to me like systems with a finite number of interacting particles don't approach equilibrium, while systems with an infinite number of particles do. That's certainly no useful physical distinction. 


#134
Dec811, 02:55 PM

P: 476

Notice that the own Brussels school (leaded by the Nobel laureate) also pretended to derive irreversibility from reversible laws, but after about four decades of futile efforts they finally understood that so one derivation is impossible, aplogized by past mistakes and wrong approaches, and in latter years they propose irreversible generalizations of QM as in the references cited. Moreover, recall that most of statistical mechanics of equilbrium is done in the thermodynamic limit. Of course, nobody is saying you that the resulting thermodynamic formulae only apply to «systems with an infinite number of particles». {*} This is so nonsensical as claiming that the second law of thermodynamics can be derived from the first law. 


#135
Dec811, 05:12 PM

P: 13

i would have answered: Energy is the ability to move (or better said to deform a frame). The ordered movement of microparticles is regarded macro as useful work, the chaotic one is regarded macro as heat. Probably, i would have been expelled from the class :)) (with a sudden lowering of my entropy, of course) 


#136
Dec811, 05:33 PM

P: 755

I don't say that the TDL doesn't give the right answers for finite systems. I just say, it can't be used in explaining them. 


#137
Dec911, 06:02 AM

P: 476

Of course, if you apply some of the «mathematical funambulism» so popular in a part of the socalled open systems quantum literature, then you can prove anything that you want... For this reason, the Brussels school (and others serious guys) now{*} start from an irreversible equation for the isolated system (a generalization of QM) and then obtain the correct irreversible equation for the open subsystem. I am so tired of the plain nonsense written in part of the literature on irreversibility that I plan to write a paper probably titled «mathematical funambulism on the theories of irreversibility» or something as that. But not now. Now I am with a paper that generalizes the first and second law of thermodynamics to open systems (yes also in this topic many literature in open systems is wrong). There are several subtle technical issues in the meaning of the TDL in their work that you fail to understand, this limit is not being taken to approximate the equation from other. It is being taken to eliminate some spurious nonMarkovian effects related to the evolution of correlations in the multiparticle system (which does not follow the Liouville equation). The reason which they take this limit is also related to the fact that the exact mathematical nature of the extended space is not still wellunderstood, and neither them nor any mathematician knows how to obtain the specific spectral decomposition in a pure ab initio fashion. Although in the same volume in Adv. Chem. Phys. a mathematician claims to obtain the spectral decomposition using a new algebra, without appealing to the TDL anymore. In my own view (sometimes discussed with relevant member of the Brussels school including the Nobel laureate himself) the resulting irreversible equation is the result of bifurcation points in the extended Liouville space, but for LPSs the nonMarkovian terms are lost and the irreversibility generated by those points mimics what would obtain from a fictitious TDL. That is, the TDL is a simple way to introduce the elements lost by the Markovinization. It is a kind of trick to obtain some results, althought you pretend to take it seriously even after being warned to not do it. This is not very different from starting from Newtonian p=mv and then obtaining the relativistic momentum by doing a trick m→m(v). Evidently, the analogy is not complete, specially because the math behind SR is wellunderstood and easy and such tricks are not more needed to obtain a relativistic momentum. It is not very different from the TDL in equilibrium SM. This trick is used to simplify some mathematical derivations otherwise would be very difficult to do or without rigor (or both). {*} As said they did your same mistake in the past 


#138
Dec911, 06:15 AM

P: 5,462

You have in another post commented upon mathematical exactitude, but offer the highly restricted formulae for the First Law since the integration of both dQ and dW is, in general, path dependent. Secondly none of the time dependent processes you mention apply to my comment. They all apply to energy transport within a system and fail at the interface between systems, which is what I am talking about. What I am referring to is another facet of the 'action at a distance' problem, which I am sure you are familiar with. This goes much deeper than schoolboy thermodynamics. 


#139
Dec1011, 07:03 AM

P: 476

I do not understand what is the link between what you say about dQ and dW and what I wrote dQ/dt and dW/dt I do not understand why you say that the time dependent processes I mentioned apply to energy transport within a system and fail at the interface between systems when dU/dt = d_{e}U/dt = dQ/dt + dW/dt the subscript «e» meaning «external». I.e., the above expression gives the changes in internal energy due to flows through the boundary surface that encloses the system volume. The above expression does not apply to energy transports inside the system. The corresponding expression for changes in the energy due to internal processes is d_{i}U/dt = 0 which is another way to state conservation of energy. And, finally, I miserable fail to understand what do you mean by «another facet of the 'action at a distance' problem» 


#140
Dec1111, 01:55 PM

PF Gold
P: 707

Like Juanrga, I do not know your meaning of "fail at the interface between systems". To me this is a boundry for mass, but not thermal energy. If by design, this interface can represent a storage of, and a speed control for energy moving between systems A and B. As mentioned before, any number of subsystems within a design. Again, thanks. I am learning a lot from this thread. 


#141
Dec2111, 11:35 AM

P: 5,462




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