"When the pH is lowered (that is, on raising the chemical potential, μ, 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." https://
patentimages.storage.googleapis.com/12/1d/09/0fb416e99018cf/US5393602.pdf

This is the upper picture here:

https://pubs.acs.org/cms/10.1021/jp972167t/asset/images/medium/jp972167tf00016.gif

We decrease the pH, the system lifts the weight, we increase the pH, the system returns to its initial state and a new lifting can start. The work we possibly waste in decreasing and increasing the pH can be reduced to zero if the process is carried out
quasistatically. Then lifting the weight is the net work involved in the isothermal cycle, in obvious violation of the second law of thermodynamics.

Systems of this kind are commonplace:

"Gels are known to change their volume in response to alteration of the environmental parameters. The change in volume results from the absorption or release of the fluid and may reach hundreds and even thousands percent. Often it is accompanied by
considerable swelling force. Gels that demonstrate substantial (and often abrupt) volume change in response to small environmental change and gels that are selective to a specific stimulus are called stimuli-responsive or responsive gels (SRGs)...The
amount of mechanical work that the gel is able to produce is important for applications where the gel is employed as an actuator. The work is proportional to both generated force and displacement..." https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5365095/

"Extraction of mechanical work from stimuli-responsive molecular systems and materials. Molecular switches and advanced molecular motors, which are the elementary building blocks for the construction of molecular machines, have been recently integrated
into soft materials in order to generate macroscopic actuation under various types of external stimulations." https://hal.science/hal-03418854/document

In most cases the mechanical work is extracted under isothermal conditions, and this, although still not a proof per se, is a strong suggestion that the second law of thermodynamics is violated (the extracted mechanical work is arguably greater than the
work wasted in activating and deactivating the stimulus). Will theoretical physicists and theoretical chemists ever consider a stimulus-responsive system producing mechanical work isothermally? No. Such a system acts like the face of Medusa the Gorgon -
on seeing it, theoreticians get petrified and never recover.

Pentcho Valev https://twitter.com/pentcho_valev

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The Clausius statement of the second law of thermodynamics:

"Heat can never pass from a colder to a warmer body without some other change connected therewith, occurring at the same time." https://quotefancy.com/quote/1636945/Rudolf-Clausius-Heat-can-never-pass-from-a-colder-to-a-warmer-body-without-some-other

This version of the second law of thermodynamics is very popular because, like "Entropy always increases", it makes no sense (scientists love nonsensical statements because they are invincible):

Clifford Truesdell, The Tragicomical History of Thermodynamics, 1822–1854, p. 333: "Clausius' verbal statement of the "Second Law" makes no sense, for "some other change connected therewith" introduces two new and unexplained concepts: "other change"
and "connection" of changes. Neither of these finds any place in Clausius' formal structure. All that remains is a Mosaic prohibition. A century of philosophers and journalists have acclaimed this commandment; a century of mathematicians have shuddered
and averted their eyes from the unclean." https://www.amazon.com/Tragicomical-Thermodynamics-1822-1854-Mathematics-Physical/dp/1461394465

Here is an oversimplified presentation of Clausius' 1850 argument:

Premise: Heat can never pass from a colder to a warmer body SPONTANEOUSLY.

Conclusion: Heat can never pass from a colder to a warmer body IN A QUASI-STATIC PROCESS.

The conclusion does not follow from the premise (the argument is invalid). Clausius' 1950 text:

Rudolf Clausius: "Carnot assumed, as has already been mentioned, that the equivalent of the work done by heat is found in the mere transfer of heat from a hotter to a colder body, while the quantity of heat remains undiminished. The latter part of this
assumption--namely, that the quantity of heat remains undiminished--contradicts our former principle, and must therefore be rejected...It is this maximum of work which must be compared with the heat transferred. When this is done it appears that there is
in fact ground for asserting, with Carnot, that it depends only on the quantity of the heat transferred and on the temperatures t and tau of the two bodies A and B, but not on the nature of the substance by means of which the work is done...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. At the end of the operations both bodies are in their original condition; further, the work produced will have exactly counterbalanced the work done, and
therefore, by our former principle, the quantity of heat can have neither increased nor diminished. The only change will occur in the distribution of the heat, since more heat will be transferred from B to A than from A to B, and so on the whole heat
will be transferred from B to A. By repeating these two processes alternately it would be possible, without any expenditure of force or any other change, to transfer as much heat as we please from a cold to a hot body, and this is not in accord with the
other relations of heat, since it always shows a tendency to equalize temperature differences and therefore to pass from hotter to colder bodies." Ueber die bewegende Kraft der Wärme, 1850 http://www.mdpi.org/lin/clausius/clausius.htm

Pentcho Valev https://twitter.com/pentcho_valev

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The following argument is valid:

Premise: The second law of thermodynamics.

Corollary: A catalyst (enzyme) accelerates the forward and backward reaction rates "equally", "by the same factor".

Professors diligently teach that a catalyst (enzyme) accelerates the forward and backward reaction "equally", "by the same factor", but avoid explaining that this is a corollary of the second law of thermodynamics. I have only found three cases where the
second law is explicitly mentioned:

"In the presence of a catalyst, both the forward and reverse reaction rates will speed up equally, thereby allowing the system to reach equilibrium faster. However, it is very important to keep in mind that the addition of a catalyst has no effect
whatsoever on the final equilibrium position of the reaction. It simply gets it there faster...If the addition of catalysts could possibly alter the equilibrium state of the reaction, this would violate the second rule of thermodynamics." https://courses.
lumenlearning.com/introchem/chapter/the-effect-of-a-catalyst/

"The second law of thermodynamics describes why a catalyst does not change the chemical equilibrium of a reaction." https://en.wikipedia.org/wiki/Catalysis

"Suppose that, as indicated in the figure, the catalyst affects only the forward reaction. In its presence, the sum of the forward rates would clearly be larger than otherwise, while the backward rate would be unchanged. The position of equilibrium would
therefore shift to the right, by the law of mass action. If we suppose further that the reaction produces heat q when it occurs, then a violation of the second law would be possible. We first allow equilibrium to be reached without the catalyst...and
then add the catalyst, and heat δq is produced as the equilibrium is shifted. This heat is used to run a machine, and thus do work, cooling the system back to its original temperature in the process. We then remove the catalyst and the equilibrium
shifts back. Heat δq is now extracted from the surroundings, which must warm the system back to the ambient temperature. A cycle has therefore been completed for which the net effect has been the isothermal conversion of heat energy into work, and a
perpetual motion machine of the second kind has been found. We conclude that the supposed situation is impossible and that the catalyst must accelerate the forward and backward reactions equally." https://dtk.tankonyvtar.hu/bitstream/handle/123456789/
8903/B9780120442621500128.pdf

Why do professors avoid teaching that "catalysts accelerate forward and reverse reaction equally" is a corollary of the second law? Because the corollary is absurd - this can easily be shown both theoretically and experimentally. Some students will
discover the absurdity sooner or later, and then two scenarios are conceivable:

1. If students don't know that the absurdity is a corollary of the second law of thermodynamics, they will only disprove their professor's teaching. Not a big deal.

2. If students do know that the absurdity is a corollary of the second law of thermodynamics, they will disprove the second law (logic forbids the combination "true premise, absurd corollary"). And this is a huge deal.

Pentcho Valev https://twitter.com/pentcho_valev

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"The pH-induced bend and straight reciprocating motion occurs periodically with fast speed in acid and alkali solution alternatively...this soft polymer film actuator exhibited a tensile strength of 74 MPa and acted as an actuator for driving a high
weight load of 1600 times its own weight." https://www.sciencedirect.com/science/article/abs/pii/S0032386120301105

So one increases and decreases the pH periodically and in each isothermal cycle the polymer lifts a weight 1600 times its own weight. Theoretical physicists and theoretical chemists:

https://content.api.news/v3/images/bin/c1700fd7feb901b86db8e30a175a9e1c

Pentcho Valev https://twitter.com/pentcho_valev

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