The crucial fact that allows Urry's polymers to violate the second law
is that they ABSORB protons on stretching. This is somewhat
paradoxical: one expects the pKa of carboxyl groups to decrease as the
distance between them increases and accordingly the polymer to RELEASE
protons on stretching:

https://data.epo.org/publication-ser...9&iepatch=.pdf
Dan Urry (pp. 14-15): "When the pH is lowered (that is, on raising the
chemical potential, mu, of the protons present) at the isothermal
condition of 37°C, these matrices can exert forces, f, sufficient to
lift weights that are a thousand times their dry weight. This is
chemomechanical transduction, also called mechanochemical coupling.
The mechanism by which this occurs is called a hydration-mediated
apolar-polar repulsion free energy and is characterized by the
equation 0(dmu/df)_n; that is, the change in chemical potential with
respect to force at constant matrix composition is a negative
quantity. Such matrices take up protons on stretching, i.e.,
stretching exposes more hydrophobic groups to water which makes the
COO- moieties energetically less favored. This is quite distinct from
the charge-charge repulsion mechanism for mechanochemical coupling of
the type where (dmu/df)_n0 and where stretching of such matrices
causes the release of protons."

Pentcho Valev wrote:

Macroscopic contractile polymers designed by Dan Urry contract and
lift a weight as one adds protons (H+) to the system (the force of
contraction increases as the pH of the system decreases):

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, p. 11025, fig. 16A

Then (the polymer is contracted) one can remove the same amount of
protons, the pH of the system would increase, the force of contraction
would decrease and the work one would spend to stretch the polymer and
restore its initial (stretched) state would be less than the work
gained previously. The net work gained from contraction and subsequent
stretching is positive. So far the second law seems to be violated
but:

The above balance does not take into account the work involved in
adding protons to the system and removing them subsequently. Note that
one GAINS work as one transfers H+, isothermally and reversibly, to
the polymer-containing system from a reservoir at higher H+
concentration, but then LOSES work as one moves the same amount of H+
back to the reservoir. The behaviour of Urry's polymers - they absorb H
+ as they stretch and release H+ as they contract - is such that the
net work gained from adding protons to the system and removing them
subsequently is positive again:

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, p. 11020: "In short,
stretching causes an uptake of protons."

"Stretching causes an uptake of protons" implies that, as one
initially adds protons to the systems in order to increase the
contraction force, the H+ concentration difference between the
reservoir and the system is relatively GREAT - accordingly, one gains
A LOT of work. "Stretching causes an uptake of protons" also implies
that, as one subsequently moves the protons back to the reservoir, the
polymer is contracted and the H+ concentration difference between the
reservoir and the system is SMALLER - accordingly, one loses LESS
work.

The net work extracted from the cycle is positive - the second law of
thermodynamics is violated.

Pentcho Valev