Perhaps the most vulnerable version of the second law of thermodynamics is:

"Catalysts do not shift chemical equilibrium."

Consider the dissociation-association reaction

A - B + C

which is in equilibrium. Let us assume that the forward reaction

A - B + C

is exothermic while the reverse

B + C - A

is endothermic. We add a catalyst, e.g. a macroscopic catalytic surface, and catalytic centers on the surface start splitting A so efficiently that the rate of the forward (dissociation) reaction increases by a factor of, say, 745492. Here is an illustration:

https://www.youtube.com/watch?v=aQ0THXw0KtI
H2 dissociation on an alloy

If the second law of thermodynamics is obeyed, the catalyst must increase the rate of the reverse (association) reaction by exactly the same factor, 745492. But this is obviously unrealistic, even idiotic - the probability that a B molecule and a C molecule will hit the catalytic center simultaneously, so that the center can combine them, could be vanishingly small! In the extreme, if the reverse reaction is diffusion-controlled (roughly speaking, any encounter of B and C produces A), the catalyst will be unable to accelerate it at all!

The second law is obviously violated - even at equilibrium, there will be local temperature and concentration gradients at the catalytic surface that can in principle be harnessed to do work.

Actually scientists have always known that catalysts do shift chemical equilibirum:

https://www.facebook.com/ParadigmEne...49600938581128
"For 50 years scientists have seen in experiments that some monomers and dimers split apart and rejoin at different rates on different surfaces. The eureka moment came when we recognized that by placing two different surfaces close together in a way that effectively eliminates the gas cloud, the energy balance would be different on each of the two surfaces. One surface would have more molecules breaking apart, cooling it, while the other surface would have more molecules joining back together, warming it."

The second-law-violating effect is presented by Wikipedia as a fact:

https://en.wikipedia.org/wiki/Epicatalysis
"Epicatalysis is a newly identified class of gas-surface heterogeneous catalysis in which specific gas-surface reactions shift gas phase species concentrations away from those normally associated with gas-phase equilibrium. [...] A traditional catalyst adheres to three general principles, namely: 1) it speeds up a chemical reaction; 2) it participates in, but is not consumed by, the reaction; and 3) it does not change the chemical equilibrium of the reaction. Epicatalysts overcome the third principle..."

https://en.wikipedia.org/wiki/Duncan%27s_Paradox
"Consider a dimeric gas (A2) that is susceptible to endothermic dissociation or exothermic recombination (A2 - 2A). The gas is housed between two surfaces (S1 and S2), whose chemical reactivities are distinct with respect to the gas. Specifically, let S1 preferentially dissociate dimer A2 and desorb monomer A, while S2 preferentially recombines monomers A and desorbs dimer A2. [...]

http://upload.wikimedia.org/wikipedi...SLTD-Fig1c.jpg

In 2014 Duncan's temperature paradox was experimentally realized, utilizing hydrogen dissociation on high-temperature transition metals (tungsten and rhenium). Ironically, these experiments support the predictions of the paradox and provide laboratory evidence for second law breakdown." [end of quotation]

Parpetual-motion machines based on the property of catalysts to shift chemical equilibrium have even entered a commercialization phase:

https://www.google.com/patents/US9212828
"An Epicatalytic Thermal Diode (ETD) includes one or more ETD cells. Each cell comprises first and second surfaces with a cavity between them, which contains a gas that is epicatalytically active with respect to the pair of surfaces. The surfaces chemically interact with the gas such that the gas dissociates at a faster rate proximate to the first surface than it does proximate to the second surface. Thus, a steady-state temperature differential between the first surface and the second surface is created and maintained.. In various applications, multiple ETD cells are connected in series and/or parallel."

http://aip.scitation.org/doi/abs/10.1063/1.4954971
"Recently, a new mode of gas-surface heterogeneous catalysis (epicatalysis) has been identified, having potential applications ranging from industrial and green chemistry to novel forms of power generation. This article describes an inexpensive, easily constructed, vacuum-compatible apparatus by which multiple candidate gas-surface combinations can be rapidly screened for epicatalytic activity."

Pentcho Valev