"Diffusion-controlled (or diffusion-limited) reactions are reactions that occur so quickly that the reaction rate is the rate of transport of the reactants through the reaction medium (usually a solution). As quickly as the reactants encounter each other, they react. The process of chemical reaction can be considered as involving the diffusion of reactants until they encounter each other in the right stoichiometry and form an activated complex which can form the product species. The observed rate of chemical reactions is, generally speaking, the rate of the slowest or "rate determining" step. In diffusion controlled reactions the formation of products from the activated complex is much faster than the diffusion of reactants and thus the rate is governed by collision frequency." https://en.wikipedia.org/wiki/Diffus...olled_reaction

Can a catalyst accelerate a diffusion-controlled reaction? Obviously not - catalysts do not accelerate diffusion. On the other hand, nothing prevents the catalyst from accelerating the reverse reaction, which means shifting the equilibrium and is tantamount to violating the second law of thermodynamics:

Consider the association-dissociation reaction

A + B - C

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

A + B - C

is diffusion-controlled. The reverse

C - A + B

is not diffusion-controlled, obviously.

We add a catalyst, e.g. a macroscopic catalytic surface, and it starts splitting C so efficiently that the rate of the reverse (dissociation) reaction increases by a factor of, say, 745492. If the second law of thermodynamics is obeyed, the catalyst must increase the rate of the forward (association) reaction by exactly the same factor, 745492, which is impossible - the catalyst cannot accelerate the forward reaction at all!

The forward reaction may not be diffusion-controlled and the catalyst may be able to accelerate it to some extent, but if the diffusion factor still plays some role in determining the rate of the forward reaction, it would be unrealistic, even idiotic, to assume that the catalyst increases both rates - of the forward and reverse reaction - by a factor of 745492.

Catalysts (enzymes) can violate the second law of thermodynamics by accelerating reversible chemical reactions in one direction and failing to produce THE SAME acceleration in the opposite direction. In such cases, even at equilibrium, there will be local temperature and concentration gradients (e.g.. 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/US20140352682
"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."

That catalysts can shift chemical equilibrium was my first heretical idea, about 20-25 years ago. I believed my argument was convincing and enthusiastically submitted a short paper to Nature - they rejected it without reading it (let alone giving it to referees). My efforts to publish continued, mainly in The Journal of Physical Chemistry, and I was also active on Internet forums. The main result was this:

http://bip.cnrs-mrs.fr/bip10/valevfaq.htm
Athel Cornish-Bowden 1998: "Reading Mr Valev's postings to the BTK-MCA and other news groups and trying to answer all the nonsense contained in them incurs the risk of being so time-consuming that it takes over one's professional time completely, leaving none for more profitable activities. On the other hand, not answering them incurs the even greater risk that some readers of the news group may think that his points are unanswerable and that thermodynamics, kinetics, catalysis etc. rest on as fragile a foundation as he pretends. [...] Can a catalyst shift the position of an equilibrium? No. Absolutely not if it is a true catalyst present at very low concentrations. If it is present at a concentration comparable with that of one or more of the reactants then it may appear to shift the position of equilibrium by mass action effects. However, when it does this it is acting as a reactant, not as a catalyst. Mr Valev's claims to have shown otherwise..."

Pentcho Valev