You are here:
Home Jack Sarfatti's Blog Maxwell Relations in Thermodynamics & 2nd Law 4-13-12 London

The Gibbs Free Energy G is a Cartan 0-form

dG is an exact 1-form

The thermodynamic Maxwell Relations MR say that

d^2G = 0

d^2 = 0

That is a vanishing “curl” Cartan 2-form.

Now when G is a multiple-valued scalar 0-form field for topological reasons - the thermodynamic lumped coarse-grained parameter manifold its defined over has topological obstructions with “holes” - non-overlapping homotopy/homology “gauge orbits” (see Hagen Kleinert’s works for rigorous math)

There is induced a new LOCAL GAUGE POTENTIAL 1-form A

i.e. we now have

dG + A

where

dA Cartan 2-form =/= 0

and that’s your violation of MR.

That’s what you are seeing.

It’s analogous to an electromagnetic field 2-Form F and to the gravity curvature 2-Form R.

It’s a thermodynamic effective gauge field and there is probably a local symmetry group for it.

This is basically the idea in my 1969 PhD in more sophisticated form - I did not know Cartan forms back then and was groping.

In any case, Hagen Kleinert has the details.

Now what the micro-mechanism is - is another story.

From this POV there is no violation of 2nd Law of Thermo - just a deeper understanding of it.

Note that in the EM case, the static Coulomb field is made of coherent Glauber states of longitudinal & timelike virtual photons.

Crystal lattices are made of coherent Glauber states of virtual phonons.

Non-radiating magnetic near fields are coherent states of virtual transverse polarized photons.

curl A =/= 0

Only far field radiation has real transverse (zero rest mass) photons.

Similarly in this thermodynamic case? - New physics here!

On Apr 13, 2012, at 1:19 PM, JACK SARFATTI wrote:

On Apr 13, 2012, at 12:48 PM, This email address is being protected from spambots. You need JavaScript enabled to view it.

Jack,

Do you agree with the following:

(Assuming temperature constant conditions)

If strain and magnetization are single valued functions of stress and H-field (state functions), and the MR for these variables is violated, then:

1. The Gibbs free energy is NOT a single valued function of stress and H-field (i.e., not a state function)

Right

2. The Kelvin Statement (of the 2nd law) is violated.

That’s the question - maybe not. I mean it may tacitly assume G is single-valued. The math was not really known in his time.

I think this is easy to show.

In a message dated 4/12/2012 8:50:17 A.M. Eastern Daylight Time, This email address is being protected from spambots. You need JavaScript enabled to view it.

10-4 however, it’s now more clear to me that you never have to say that violation of Maxwell Relations is tantamount to violation of the Second Law of Thermodynamics - this is not only politically expedient, but I think physically correct. Remember Eddington! ;-)

On Apr 12, 2012, at 1:22 PM, This email address is being protected from spambots. You need JavaScript enabled to view it.

Hi Jack,

Just want to clarify. We have not yet performed an actual "over-unity" test. Only actual "over-unity" test so far is UMD experiment.

What we have measured are fairly large MR discrepancies in the magnetomechanical system which (given overall losses can be minimized) will be capable of "over-unity" operation.

In a message dated 4/12/2012 5:11:16 A.M. Eastern Daylight Time, This email address is being protected from spambots. You need JavaScript enabled to view it.

Pelligrini et-al (North Eastern University, Boston) report such violations in magnetostrictive materials at kilohertz frequencies with an anomalous seemingly over-unity net energy output. Their experiments and allegedly similar ones at a US Navy lab seem to violate the 19th Century Clausius formulation of the Second Law of Thermodynamics. These people are not cranks so what they are seeing needs understanding. Also there are evidently practical energy payoffs if the claims are substantiated.

.

My basic point is elementary from section 10.2 of Penrose RR.

The Maxwell Relations are generally

<8df17122883a7607a3af0937e31caef6.png>

This corresponds to a vanishing curl for the gradients of the potentials.

Some specific cases are:

<7cc3f7f7b80bcba4ba4a26948e933ab8.png>

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

<ScreenShot2012-04-12at9.37.56AM.png>

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

The basic thermodynamic potentials U, H, A, G are Cartan 0-form (scalar fields) of thermodynamic parameters.

Their Cartan 1-form “vector fields,” e.g. dU below where d is the Cartan exterior derivative in thermodynamic parameter space of natural variables - not physical space-time where what we are discussing are “fibers” in sense of mathematics of fiber bundles.

<ScreenShot2012-04-12at10.09.14AM.png>

<ScreenShot2012-04-12at9.41.40AM.png>

Now we certainly have non-vanishing curls in electrodynamics. This requires a transverse polarized vector potential A in addition to the longitudinal scalar potential. Obviously, something similar is needed to explain Pelligrini’s et-al’s data. Curiously, I introduced such a quantity for superfluid helium turbulence in my 1969 Ph..D. dissertation with Fred W. Cummings (of the Jaynes-Cummings model now ubiquitous in quantum information theory models of strings of qubits). The timelike scalar and longitudinal part of A are constrained together by U1 local gauge invariance.

In terms of Cartan forms d^2 = 0, therefore, the above thermodynamic Cartan 1-forms are not exact 1-forms in Pelligrini’s data. They are not even closed 1-forms because they have local non-vanishing 2-form exterior derivatives.

Now Penrose says that the basic Maxwell relations correspond to C^2 smoothness in the thermodynamic potentials. Obviously, this is violated in Pelligrini’s case assuming that his measurements are good.

Clearly, there is no violation of the 2nd Law of Thermodynamics which must be generalized to include the quasi local gauge field A. A similar trick is used by Frank Wilczek for 2D anyons.

The A field corresponds to topological obstructions and what Hagen Kleinert means by singular “multi-valued fields,” i.e. different homotopy/homology classes. The thermodynamic potential Cartan 0-form scalar fields are no longer single-valued functions in a simply-connected thermodynamic parameter manifold. Indeed, the Bohm-Aharonov and Berry phase effects may be relevant here?

Category: MyBlog

Written by Jack Sarfatti

Published on Friday, 13 April 2012 05:45

't Hooft 100 Year Star Ship Abner Shimony accelerometers action-reaction principle Aephraim Sternberg Alan Turing Albert Einstein Alpha Magnetic Spectrometer American Institute of Physics Andrija Puharich Anthony Valentin Anton Zeilinger Antony Valentini anyon Apple Computer Artificial Intelligence Asher Peres Back From The Future Basil Hiley Bell's theorem Ben Affleck Ben Libet Bernard Carr Bill Clinton black body radiation Black Hole black hole firewall black hole information paradox black holes Bohm brain waves Brian Josephson Broadwell Cambridge University Carnot Heat Engine Central Intelligence Agency CIA Clive Prince closed time like curves coherent quantum state Consciousness conservation laws Cosmic Landscape Cosmological Constant cosmology CTC cyber-bullying Dancing Wu Li Masters Dark Energy Dark Matter DARPA Daryl Bem David Bohm David Deutsch David Gross David Kaiser David Neyland David Tong de Sitter horizon Dean Radin Deepak Chopra delayed choice Demetrios A. Kalamidas Demetrios Kalamidas Dennis Sciama Destiny Matrix Dick Bierman Doppler radars E8 group Einstein's curved spacetime gravity Einstein's happiest thought electromagnetism Eli Cartan EMP Nuclear Attack entanglement signals ER=EPR Eric Davis Ernst Mach ET Eternal Chaotic Inflation evaporating black holes Facebook Faster-Than-Light Signals? fictitious force firewall paradox flying saucers FQXi Frank Tipler Frank Wilczek Fred Alan Wolf Free Will G.'t Hooft Garrett Moddel Gary Zukav gauge theory general relativity Geometrodynamics Gerard 't Hooft Giancarlo Ghirardi God Goldstone theorem gravimagnetism gravity Gravity - the movie gravity gradiometers gravity tetrads Gravity Waves Gregory Corso gyroscopes hacking quantum cryptographs Hagen Kleinert Hal Puthoff Hawking radiation Heisenberg Henry Stapp Herbert Gold Higgs boson Higgs field hologram universe Horizon How the Hippies Saved Physics I.J. Good ICBMs Igor Novikov inertial forces inertial navigation Inquisition Internet Iphone Iran Isaac Newton Israel Jack Sarfatti Jacques Vallee James F. Woodward James Woodward JASON Dept of Defense Jeffrey Bub Jesse Ventura Jim Woodward John Archibald Wheeler John Baez John Cramer John S. Bell Ken Peacock Kip Thorne Kornel Lanczos La Boheme Laputa Large Hadron Collider Lenny Susskind Leonard Susskind Levi-Civita connection LHC CERN libel Louis de Broglie Lubos Motl LUX Lynn Picknett M-Theory Mach's Principle Mae Jemison Making Starships and Star Gates Martin Rees Mathematical Mind MATRIX Matter-AntiMatter Asymmetry Max Tegmark Menas Kafatos Michael Persinger Michael Towler microtubules Milky way MIT MOSSAD multiverse NASA Nick Bostrum Nick Herbert Nobel Prize nonlocality Obama organized-stalking Origin of Inertia P. A. M. Dirac P.K.Dick P.W. Anderson Paranormal parapsychology Paul Werbos Perimeter Institute Petraeus Physical Review Letters Physics Today Post-Quantum Physics pre-Big Bang precognition presponse PSI WARS Psychic Repression qualia Quantum Chromodynamics quantum computers quantum entanglement quantum field theory quantum gravity Quantum Information Theory Quantum Theory RAF Spitfires Ray Chiao Red Chinese Remote Viewing retrocausality Reviews of Modern Physics Richard Feynman Richard P. Feynman Rindler effect Robert Anton Wilson Robert Bigelow Roger Penrose rotating black holes Roy Glauber Rupert Sheldrake Russell Targ Ruth Elinor Kastner S-Matrix Sagnac effect Sam Ting Sanford Underground Research Facility Sarfatti Lectures in Physics Scientific American Second Law of Thermodynamics Seth Lloyd signal nonlocality Skinwalker Ranch social networks space drive space-time crystal SPECTRA - UFO COMPUTER spontaneous broken symmetry SRI Remote Viewing Experiments Stanford Physics Stanford Research Institute Star Gate Star Ship Star Trek Q Stargate Starship Stephen Hawking Steven Weinberg stretched membrane string theory strong force gluons Stuart Hameroff superconducting meta-material supersymmetry symmetries telepathy Templeton The Guardian Thought Police time crystal time travel topological computers Topological Computing torsion UFO Unitarity unitary S-Matrix false? Unruh effect Uri Geller VALIS virtual particle Virtual Reality Warp Drive weak force Wheeler-Feynman WIMP WMAP WMD world crystal lattice wormhole Yakir Aharonov Yuri Milner

- November 2015(1)
- January 2015(1)
- December 2014(1)
- August 2014(2)
- July 2014(2)
- June 2014(2)
- May 2014(1)
- April 2014(6)
- March 2014(6)
- February 2014(1)
- January 2014(3)
- December 2013(5)
- November 2013(8)
- October 2013(13)
- September 2013(8)
- August 2013(12)
- July 2013(3)
- June 2013(32)
- May 2013(3)
- April 2013(6)
- March 2013(6)
- February 2013(15)
- January 2013(5)
- December 2012(15)
- November 2012(15)
- October 2012(18)
- September 2012(12)
- August 2012(15)
- July 2012(30)
- June 2012(13)
- May 2012(18)
- April 2012(12)
- March 2012(28)
- February 2012(15)
- January 2012(25)
- December 2011(29)
- November 2011(30)
- October 2011(39)
- September 2011(22)
- August 2011(41)
- July 2011(42)
- June 2011(24)
- May 2011(13)
- April 2011(13)
- March 2011(15)
- February 2011(17)
- January 2011(31)
- December 2010(19)
- November 2010(22)
- October 2010(31)
- September 2010(41)
- August 2010(30)
- July 2010(27)
- June 2010(12)
- May 2010(20)
- April 2010(19)
- March 2010(27)
- February 2010(34)