Carnot dealt with two reversible heat engines which DID NOT INTERACT.
In 1850 Clausius used NON-INTERACTING heat engines again:

http://www.mdpi.org/lin/clausius/clausius.htm
"Ueber die bewegende Kraft der Wärme", 1850, Rudolf Clausius: "If we
now suppose that there are two substances of which the one can produce
more work than the other by the transfer of a given amount of heat,
or, what comes to the same thing, needs to transfer less heat from A
to B to produce a given quantity of work, we may use these two
substances alternately by producing work with one of them in the above
process."

Below I will try to show that, by replacing NON-INTERACTION with
INTERACTION, one reaches the conclusion that the second law of
thermodynamics is false.

NON-INTERACTION means that the work-producing force generated by the
first engine, F1, is independent of the displacement, X2, in the
second engine, and vice versa. Under isothermal conditions, if the
system is closed (only energy can be exchanged with the environment),
F1 can be presented as a function of X1 and X2 and the independency
condition can be expressed as the partial derivative (dF1/dX2)_X1
being equal to zero ("partial" because X1 is kept constant):

F1 = F1(X1, X2); F2 = F2(X1, X2)

(dF1/dX2)_X1 = (dF2/dX1)_X2 = 0

It can be shown that, if the two reversible heat engines DO INTERACT,
the equation:

(dF1/dX2)_X1 = (dF2/dX1)_X2

is a consequence of the second law of thermodynamics (Kelvin's
version). Accordingly, if the partial derivatives (dF1/dX2)_X1 and
(dF2/dX1)_X2 are somehow shown not to be equal, then heat CAN,
cyclically and isothermally, be converted into work, in violation to
the second law of thermodynamics.

Consider, for instance, INTERACTING "chemical springs". There are two
types of macroscopic contractile polymers, further called Urry's (U)
and Katchalsky's (K), which on acidification (decreasing the pH of the
system) contract and can lift a weight:

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"

There is a crucial difference between U and K. Polymers designed by
Urry (U) ABSORB protons on stretching (as their length, Lu,
increases):

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."

In contrast, Katchalsky's polymers (K) RELEASE protons on stretching
(as their length, Lk, increases):

http://www.ncbi.nlm.nih.gov/pmc/arti...00645-0017.pdf
POLYELECTROLYTES AND THEIR BIOLOGICAL INTERACTIONS, A. KATCHALSKY, pp.
13-15: "Let the polymolecule be a negatively charged polyacid in a
stretched state and have a length L. Now let us add to the molecule a
mineral acid to provide hydrogen ions to combine with the ionized
carboxylate groups and transform them into undissociated carboxylic
groups according to the reaction RCOO- + H+ = RCOOH. By means of this
reaction, the electrostatic repulsion which kept the macromolecule in
a highly stretched state vanishes and instead the Brownian motion and
intramolecular attraction cause a coiling up of the polymeric chains.
Upon coiling, the polymolecule contracts and lifts the attached weight
through a distance deltaL. On lifting the weight, mechanical work
f*deltaL was performed... (...) FIGURE 4: Polyacid gel in sodium
hydroxide solution: expanded. Polyacid gel in acid solution:
contracted; weight is lifted."

Let us assume that two macroscopic polymers, one of each type (U and
K) are suspended in the same system. At constant temperature, IF THE
SECOND LAW IS TRUE, we must have

(dFu / dLk)_Lu = (dFk / dLu)_Lk

where Fu0 and Fk0 are work-producing forces of contraction. The
values of the partial derivatives (dFu/dLk)_Lu and (dFk/dLu)_Lk can be
assessed from experimental results reported on p. 11020 in Urry's
paper referred to above. As K is being stretched (Lk increases), it
releases protons, the pH decreases and, accordingly, Fu must increase.
Therefore, (dFu/dLk)_Lu is positive. In contrast, as U is being
stretched (Lu increases), it absorbs protons, the pH increases and Fk
must decrease. Therefore, (dFk/dLu)_Lk is negative. One partial
derivative is positive, the other negative: this proves that the
second law of thermodynamics is false.

Pentcho Valev