i.e. use 1/T* = 1/T + 1/X in Carnot's formula for max efficiency rather than T* = T + X

The analogy above is is to Kirchoff's circuit laws for resistance/impedance. Eq 1 is for a series connection. The above is for a parallel processing connection that seems more natural because the different intensive parameters are orthogonal dimensions in abstract thermodynamic phase space. Also if there are order parameters from spontaneous symmetry breakdown or from topology then there will also be Berry phase shifts.

Remember TdS and Xidx^i all have same dimensions as energy, so the dimensions must be consistent in the sums.

On Feb 9, 2012, at 12:01 AM,

Hi Jack,

Just to clarify one point:

The Navy experimentalists did not allege "anomalous energy output". They reported as much as 50% discrepancies in the (d and d*) Maxwell relations:

http://jap.aip.org/resource/1/japiau/v109/i7/p07A922_s1?isAuthorized=no

The University of Maryland experimentalists reported an isothermal anomalous energy output (mechanical work output > magnetic work input) associated with Maxwell (d and d*) discrepancies:

http://adsabs.harvard.edu/abs/2011SMaS...20g5008Y

"If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations—then so much the worse for Maxwell's equations. If it is found to be contradicted by observation—well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation." - Eddington

This is admittedly half-baked as I have not digested the details of Gerry Pellegrini's reports of the US Navy work on what seems to be anomalous energy production in one-dimensional magnetostrictive filaments in materials. Gerry worries that the Second Law of Thermodynamics seems to be violated because of work output under isothermal conditions in a closed cycle in which allegedly dissipation is not significant. This is a bit like the cold fusion claims.

1) there is still little understanding of far-from-thermal equilibrium physics. It's pretty much like quantum gravity and string theory really.

We have fluctuation-dissipation theorems, but they are only near equilibrium. This is analogous to first order perturbation theory of a small huv spin 2 tensor field on a non-dynamical Minkowski space-time as in Feynman's CIT Gravity Lectures. We also have Haken's work on pumped laser type systems, but none of that seems applicable to the alleged US Navy "over-unity"? data.

2) assuming that the Navy data is quasi-static reversible so that the Carnot heat engine idea is a reasonable place to start. We know that the maximal efficiency in a closed cycle (for ignorable irreversibility) in a closed cycle

MAX efficiency = (Work Output)/(Energy Input) = 1 - T(output)/T(input)

http://en.wikipedia.org/wiki/Carnot_cycle

Therefore, if the condition is isothermal we get ZERO. In fact, the Navy guys seem to be getting something positive out, if I understand Gerry right?

OK first we have conjugate variables in thermo T (absolute Kelvin) temperature is intensive conjugate to extensive entropy

intensive pressure conjugate to extensive volume - this extends to electromagnetic properties.

Then we have for example for the differential of internal energy of the material

Here the Xi are the generalized forces corresponding to the external variables xi

X are intensive x are extensive

I conjecture that in the general case we have a higher dimensional space in which the P-V plane is a slice.

Carnot's formula then generalizes to

Eq 1

In Gerry's case in particular

Why permeability of free space? Should it not be permeability of the material that could be meta-material? Similarly can add for electrostriction, for piezo electromagnetism etc.

If the above formula I have concocted out of thin air, stolen from the future like Jack and the Beanstalk ;-) is crazy enough to be true then we see:

1) no problem when the two absolute temperatures T are the same.

2) the fraction on the RHS can be negative. This would result in apparent over unity sucking out the internal energy of the material so there is no contradiction with energy conservation first law of thermo. The material would self-destruct in such a case undergoing some kind of dramatic phase transition.

3) the fraction can be negatively large causing the efficiency itself to go negative. What does that mean? Well, it might mean exotic matter negative energy output needed to make warp drive and wormhole star gates?

As I said this is all very half-baked at this point.