🚀 go-pugleaf

Take a suspended and stretched spring. It can lift a weight as it
contracts, that is, we GAIN work. However, in order to restore the
initial stretched state of the spring, we must SPEND work so there is
no net gain. If both contraction and stretching are carried out in a
reversible fashion, the net work gained at the end of the cycle is
zero.

Consider again a suspended and stretched spring but this time it is
"chemical", that is, we have one of the macroscopic contractile
polymers described by Dan Urry in:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007 - 11028
Dan W. Urry, "Physical Chemistry of Biological Free Energy
Transduction As Demonstrated by Elastic Protein-Based Polymers"

If, before contraction, we add acid (H+) to the system, the force of
contraction and, respectively, the work gained as the polymer
reversibly contracts increase. Then, just before stretching, we remove
the added H+ from the system: the force of contraction and,
respectively, the work spent as we reversibly stretch the polymer
decrease. At the end of the cycle, THE NET WORK GAINED FROM
CONTRACTION AND STRETCHING IS POSITIVE.

So far things go against the second law of thermodynamics but the
complete account requires that the net work gained from adding H+ to
and removing H+ from the system be evaluated. If it is positive or
zero, the second law is definitively violated. If it is negative, the
second law is saved for the moment.

In the absence of the polymer, adding H+ to and removing the same
amount of H+ from the system, in a reversible fashion, would amount to
zero net work gained. The polymers designed by Urry, however, release H
+ as they contract, and absorb H+ as we stretch them. It is easy to
see (for people experienced in electrochemistry at least) that this
makes the net work gained from reversibly adding H+ to and then
removing the same amount of H+ from the system POSITIVE.

Conclusion: The reversible cycle:

1. The polymer is stretched. We add H+ to the system.
2. The polymers contracts and lifts a weight.
3. We remove the same amount of H+ from the system.
4. We stretch the polymer and restore the initial state of the system.

violates the second law of thermodynamics.

Pentcho Valev
pvalev@yahoo.com