Retarded potentials and entropy

[lalbatros]

Selecting retarded potentials as solutions of the Maxwell's equations or of more generally the electrodynamic equations implies selecting one arrow of time. It is normal to assume that this arrow of time is consistent with the thermodynamic arrow of time implied by the second principle of thermodynamics.

Let's assume that we "select" a very special system in which the only irreversibility would be related to the effects of retardation of the potentials. Conceiving such a system might by a little bit un-natural, but I assume this is not impossible by principle. Maybe it could be simply related to "freezing" some degrees of freedom.

If this assumption is allowed, then this would imply that the entropy of this system would increase only because of the retardation. This would suggest an entropy (term) related to retardation (choice) of the electromagnetic potentials.

I would be curious to know if such a "electromagnetic retardation" term does indeed exist.
How would it look like?

Thanks

 

[eljose79]

for your question! it is important to consider all possible explanations and implications of our theories and equations. In this case, selecting retarded potentials as solutions of the Maxwell's equations does indeed imply selecting one arrow of time. This is because the use of retarded potentials implies that the effects of an interaction propagate from past to future, following the direction of the arrow of time.

It is also reasonable to assume that this arrow of time is consistent with the thermodynamic arrow of time, as the second law of thermodynamics states that the entropy of a closed system will always increase with time.

As for the idea of a "special system" where the only irreversibility is related to the effects of retardation of the potentials, this is certainly an interesting concept. Such a system could potentially be created by freezing certain degrees of freedom, as you suggested. However, it is important to note that this would be an idealized and simplified system, as in reality, there are always other factors at play that contribute to the irreversibility of a system.

In terms of the existence of an "electromagnetic retardation" term related to entropy, this is not a commonly used term in the field of electromagnetism. However, there are certainly terms and equations that take into account the effects of retardation, such as the Lienard-Wiechert potentials. These equations describe the electromagnetic field produced by a moving charged particle, taking into account the time delay in the propagation of the field. This time delay can certainly have an impact on the entropy of a system, but it is not a separate term in itself.

Overall, while the concept of a "retardation term" related to entropy is not commonly used in electromagnetism, the effects of retardation are certainly taken into account in various equations and theories. As scientists, it is always important to continue exploring and questioning our theories to gain a deeper understanding of the natural world.