"Coonskin, did you actually read the cite? Here's the start of the
conclusion:
"Thermodynamics is not the limiting factor behind the concept of
metabolic
advantage. On the contrary, thermodynamics guarantees inefficiency in
all
metabolic processes and is silent on the possibility that inefficiency
may
be augmented in some instances."

In the body of the closely-argued text, they describe 4 and mention a
further mechanism where metabolic advantage has been apparent in
experimental studies. These include low carb and protein based diets.

He's not sure whether the observed metabolic advantage is coming from a
dietary source or from endogenous (internal) mechanisms, hence the
fence-sitting; he's absolutely clear that such an effect exists."

I read that conclusion also, it says in other words what I was saying.  
"Metabolic advantage" is with regard to possible "advantage" in weight
loss because some nutrients require more energy, calories, to metabolize
then do others.  This follows your part above:

"The presence of high quantities of dietary protein (often a feature of
low carbohydrate diets) is known to stimulate protein turnover, an
energetically costly process. However, it is unclear whether this is the
only factor, or whether it is necessary for metabolic advantage to
occur."

I used the exact same example of how different pathways have differing
energy costs.  A high protein diet uses more energy to get to cells then
does a carb or fat diet.  But this only pushes the decimal point about
some when the sum of all energy costs are totaled and subtracted from
total calorie intake.

All of this changes the fundimental truth not at all, weight loss in the
end depends on consuming fewer calories then are required for daily
activity including basic metabolism.  In principle a higher protein diet
will be a bit faster given the same calorie intake because more of those
calories are consumed in using protein compared to fat and carbs.  If a
low carb diet works it is because of this fundimentl process of mucking
about with the energy costs of different nutrition sources and related
metabolic advantages different sources engage.

A calorie is a calorie at the cell usage level.  But how many calories
are consumed getting those calories to the cell differrs depending on
how much the original source of them has to be modified to get them to
the cells and the cost in calories to carry out that process.  All
calories do not reach the cells in the same amount depending on the food
source containing them.  A low carb idet also consumes more calories to
shift internal metabolism to consuming stored fat also which is an
additional calorie cost to make it happen..