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Second Law of Thermodynamics

February 7, 2011

Inventors seem to have a fascination with Perpetual motion machines. Some believe that if they just position magnets the right way, or devise a different type of pendulum swing, their device will operate forever once it gets going. The more entrepreneurial sorts think they can extract useful, and perpetually free, energy from their devices as well. I mentioned perpetual motion machines in two previous articles (Perpetuum Mobile, August 24, 2006 and Perpetual Motion (Continued), August 28, 2006).

Scientists are skeptical of perpetual motion machines, since they defy the laws of thermodynamics. Such a machine might defy the first law of thermodynamics, which is the conservation of energy law. It may instead, or additionally, defy the second law of thermodynamics, which is a little more difficult to summarize. The second law essentially says that thermal systems will equilibrate after sufficient time. It's often expressed as the law that states that system entropy must increase and natural processes are irreversible. Supposed perpetual motion machines that violate the first or second law are classified as perpetual motion machines of the "first" or "second" kind.

The second law is an unusual law, since it involves the strange concept, entropy. Entropy became much more understandable, at least to me, in its application to information theory by Claude Shannon. As recalled by Shannon, it was John von Neumann who suggested that Shannon use the term entropy in an information context.
"You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage."[1]

My favorite summary of thermodynamics is found in the equation,
d)E - Td)S + Pd)V <= 0

which combines energy (E), temperature (T), entropy (S), pressure (P), and volume (V). The term, Pd)V is the work, and it's that nasty entropy term Td)S that says there is no such thing as a free lunch.

Physicists are especially skeptical about perpetual motion machines, since they've been developing and validating thermodynamics over the course of hundreds of years. The American Physical Society, of which I am a member, issued the following statement in 2003:
"The American Physical Society deplores attempts to mislead and defraud the public based on claims of perpetual motion machines or sources of unlimited useful energy, unsubstantiated by experimentally tested established physical principles."

The APS lawyers must have been worried about such a strong statement, but the APS skepticism is backed by the US Patent and Trademark Office in its Manual of Patent Examining Procedure (MPEP). Essentially, if you want to patent a perpetual motion machine, the patent examiner would like to see it work. I'm reminded of all those examinations for which I was required to "show all work."
"With the exception of cases involving perpetual motion, a model is not ordinarily required by the Office to demonstrate the operability of a device. If operability of a device is questioned, the applicant must establish it to the satisfaction of the examiner, but he or she may choose his or her own way of so doing." (Section 608.03)

"A rejection on the ground of lack of utility includes the more specific grounds of inoperativeness, involving perpetual motion." (Section 706.03a)
The US Patent office lumps perpetual motion machines with the following questionable items:
• An invention that changes the taste of food using a magnetic field.
• A flying machine operating on "flapping or flutter function."
• A "cold fusion" process for producing energy.
• A method for increasing the energy output of fossil fuels upon combustion through exposure to a magnetic field.
• Uncharacterized compositions for curing a wide array of cancers.
• A method of controlling the aging process.
It seems as if magnets have a special appeal to inventors. There is one strange magnetic technology with some science behind it. Transcranial magnetic stimulation appears to temporarily activate, or inactivate, parts of the brain. It may help with a variety of medical problems, and there might really be a magnetic means to make food taste better.

Some prominent physicists have devised examples of machines that appear to act as perpetual motion devices. However, they are intended as examples of how a detailed analysis will prove them wrong. Two of these are Maxwell's demon and Feynman's "Brownian ratchet." Feynman's machine, a ratchet that moves just one direction when excited by randomly moving molecules, appears to extract work from thermal fluctuations; however, a more detailed analysis shows that it will work only as long as the ratchet is cooler than the environment.

Maxwell's demon is a mythical creature that acts as a gatekeeper between two gas reservoirs. When he (or, perhaps, she) sees a hot molecule coming to the gate, he opens it to let it into one reservoir. Likewise, he allows only cool molecules to enter the other reservoir. In this way the demon generates a temperature difference. Maxwell's demon has generated a lot of publications, but the consensus is that the demon needs to "see" the particles he's supposedly sorting, and that's an external influence on the system. There are the lesser problems of the energy it takes to compute the state of a particle, and to open and close the flap.

A drinking bird toy.

Simulated perpetual motion. The drinking bird relies on the cooling effect of evaporation to drive a simple heat engine. See Ref. 2.[2]

Germano D'Abramo, a physicist and mathematician at the Istituto Nazionale di Astrofisica, Rome, Italy, known for work on Turing's Halting Problem,[3] has just published a paper on the Second Law of Thermodynamics on the arXiv Preprint Server.[4] As D'Abramo points out, the second law is not a law like F = ma. It's a statistical law, and there has been no real argument that excludes its possible macroscopic violation. Says D'Abramo, "None of Maxwell’s Demon exorcisms provides basic principles and fundamental laws of physics able to absolutely forbid the violation of the second law."[4] D'Abramo's main argument is that everyone is fixated on the Maxwell Demon model of two gas reservoirs separated by a plenum, and they've ignored other systems that may "violate" the second law.

A model system that D'Abramo proposes is the thermally-charged vacuum capacitor, which is charged from a single room temperature reservoir.[5-6] He calculates that he can extract a small amount of work (10-14 Watts) from such a capacitor, in violation of the second law. Power at this femtowatt scale would be difficult to measure; more importantly, the second-law-violating-power would be difficult to separate from other effects. This might be the thermodynamics analog of string theory - The equations are right, but the experiment is impossible.


  1. M. Tribus and E.C. McIrvine, "Energy and information," Scientific American, vol. 224, no. 9 (September 1971), pp. 178-184, as referenced in D'enes Petz, "Entropy, von Neumann and the von Neumann entropy".
  2. Miles V. Sullivan, "Novelty Device," US Patent No. 2,402,463, June, 1946
  3. Germano D'Abramo, "Asymptotic behavior and halting probability of Turing Machines," Chaos, Solitons & Fractals, vol. 37, no. 1 (July, 2008), Pages 210-214. Yes, I'm compelled to say Entscheidungsproblem. How could I resist?
  4. Germano D'Abramo, "The Peculiar Status of the Second Law of Thermodynamics and the Quest for its Violation," arXiv Preprint Server, January 26, 2011.
  5. G. D'Abramo, "Thermo-charged capacitors and the Second Law of Thermodynamics," Physics Letter A, vol. 374, no. 17-18 (April 12, 2010), pp. 1801-1805 .
  6. G. D'Abramo, "On the exploitability of thermo-charged capacitors," Physica A, vol. 390, no. 3 (February 1, 2011), pp. 482-491 .
  7. Perpetual Motion Page on Wikipedia.
  8. History of Perpetual Motion Page on Wikipedia.

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Linked Keywords: Inventor; Perpetual motion; magnet; pendulum; entrepreneur; energy; scientist; thermodynamics; first law of thermodynamics; conservation of energy; second law of thermodynamics; entropy; irreversible process; information_theory; Claude Shannon; John von Neumann; information entropy; temperature; pressure; volume; free lunch; physicists; American Physical Society; US Patent and Trademark Office; Manual of Patent Examining Procedure (MPEP); Section 608.03; Section 706.03a; Section 2107.01; Transcranial magnetic stimulation; Maxwell's demon; Richard Feynman; Brownian ratchet; ratchet; thermal fluctuations; drinking bird; Germano D'Abramo; Istituto Nazionale di Astrofisica; Turing's Halting Problem; arXiv Preprint Server; vacuum capacitor; Watts; femtowatt; string theory; experiment; Entscheidungsproblem.