On 20 Nov 2014, at 02:15, George wrote:
Hi everyone
This post is relevant to a few threads in this list
“Reversing time = local reversal of thermodynamic arrows?” and “Two
apparently different forms of entropy”.
I am sorry that I haven’t posted to this list for a while. I have
been very busy with my work.
In my latest research I have found that Quantum Mechanics, in
particular the Pauli Exclusion Principle, can be used to go around
limitations of classical physics and break the Second Law.
Papers describing the research are publicly available at
http://www.mdpi.com/1099-4300/15/11/4700
and
https://sites.google.com/a/entropicpower.com/entropicpower-com/Thermoelectric_Adiabatic_Effects_Due_to_Non-Maxwellian_Carrier_Distribution.pdf?attredirects=0&d=1
(Currently under review)
Nice to hear from you George. It has been a long time indeed. I will
take a look, but up to now, my computer refuses to open the document ...
To be frank, I doubt very much that QM could break the Second Law. If
you could sum up the reason here, it would be nice. Take your time (I
am also rather busy those days).
Best,
Bruno
These papers describe experimentally observed thermoelectric
adiabatic effects (the existence of a voltage without any heat flow,
and the existence of a temperature differential without any input
current.)
Here is some background: The story begins with a thermodynamicist of
the nineteenth century, Josef Loschmidt, who challenged Boltzmann
and Maxwell regarding the Second Law. Loschmidt argued that the
temperature lapse in the atmosphere could be used to run a heat
engine, thereby violating the Second Law. Loschmidt was wrong as
shall be explained below but it is instructive to go through his
reasoning. Loschmidt argued that the atmospheric temperature lapse
occurs spontaneously, is self renewing and is due to the decrease in
kinetic energy of molecules as they go up against the gravitational
gradient between collisions. Therefore the atmospheric temperature
decreases adiabatically with altitude and could be used to run a
heat engine.
However, Loschmidt ignored the fact that molecular energies are
distributed over a range of values and that gravity separates the
molecules according to their energy in a fashion analogous to a mass
spectrometer separating particles according to mass. Molecules with
greater energy can reach greater heights. If one assigns a
Maxwellian distribution to the molecules (exponentially decaying
function of energy), then any vertical translation of a group of
molecules results in a lowering of their kinetic energy,
corresponding to a left shift of their distribution. After the
distribution is renormalized to account for the lower density at
higher elevation, the original distribution is recovered indicating
that the gas is isothermal, not adiabatic as Loschmidt conjectured.
This effect is due to the exponential nature of the distribution. An
addition (of potential energy) in the exponent corresponds to a
multiplication of the amplitude. So Loschmidt was wrong: the
Loschmidt effect (lowering of KE with altitude) is exactly canceled
by the energy separation effect caused by gravity. However he was
only wrong with respect to gases that follow Maxwell’s distribution.
Electrical carriers in semiconductor materials are Fermions
following Fermi-Dirac statistics and the above argument does not
apply to them. When subjected to a voltage they do develop a
temperature gradient. This temperature differential is hard to
observe because it is promptly shorted by heat phonons. As
experiments at Caltech have shown (see my papers), it can be
observed in certain circumstances such as in high Z thermoelectric
materials in which electrical carriers and heat phonons are strongly
decoupled. The Onsager reciprocal of the temperature differential is
a voltage differential which has also been experimentally observed.
The two papers above describe these results in detail.
In summary, quantum mechanics, in particular the Pauli Exclusion
Principle, can be used to bypass classical mechanics in generating
macroscopic effects violating the Second Law.
Other relevant papers:
1) Hanggi and Wehner arXiv:1205.6894 show that any violation
to the Uncertainty Principle would result in a violation of the
Second Law. This does not contradict my research which shows use of
QM to violate the Second Law. The paper also suggests for
future research the reverse proposition that any violation of the
Second Law would result in a violation of the Uncertainty Principle.
This, if true, would contradict my research.
2) Lloyd, Seth, http://people.physics.anu.edu.au/~tas110/Teaching/Lectures/L5/Material/Lloyd06.pdf
. This paper discusses derivation of 2nd Law from QM.
I welcome any comment or criticism that you may have.
George Levy
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