A linear equation can always be used to model a nonlinear phenomenon.
Perhaps you mean a nonlinear curve fit can always be applied to a linear function? Since one can presume that a linear function is really just a polynomial fit where all the higher order terms are zero?
What you might also mean is that a linear equation can be used to model a non-linear phenomenon
badly with a significantly small R[sup]2[/sup] and an F-statistic that shows a p-value of insiginificance.
Is that what you meant?
Entropy is likewise nonlinear,
Again, you are confusing terms here. Entropy is a measure of the states of the system. It is not a trend with anything, except perhaps the temperature of the system.
S = Q/T is a linear expression. However if memory serves, entropy is seldom analyzed except in terms of change in entropy, so
dS = dQ/T
I do not think that
necessitates a non-linear interpretation.
In statistical thermodynamics where S is explicitly defined rather than as a change in S it is defined as:
S = k*ln(W)
Where k is boltzmann's constant
W is the number of microstates of the system.
This is a logarithmic equation with respect to the number of microstates.
But I think perhaps you mean the
change in entropy when you talk about "linear and non-linear".
and it should be intuitively obvious even if the convention is to use a simple linear equation.
Be
very very careful here, True_Blue. Remember, in curve fitting one can apply R[sup]2[/sup] terms to each of the terms in the fit equation. So if a data set fits best with no higher order terms or no exponentials, it is by definition a linear trend. This is not just a "convention", it is rooted in the mathematics.
I can always claim that a line can be fit with a linear or non-linear equation, but there is a
direct and quantifiable means by which I can tell which is the better fit.
I recommend that you either support your claims or drop this line of "reasoning".