Is inflation an entropic process? I've looked for this specific question and haven't found it so I'm posting it here.
What I am asking is whether the process of inflation itself is an entropy raising process?
The reason I am asking this is that there seems to be a lot of papers centered around the idea that somehow inflation 'explains' the low entropy initial condition or 'past hypothesis'.   If inflation is an entropy raising process then this cannot be the case, because the universe would have had to be in even lower entropy before inflation for it to happen, and that just leaves you begging the question.  The only active physicists that seem to be widely recognising that inflation makes the past hypothesis more of a mystery rather than somehow explaining it is Penrose who doesnt believe in inflation) and Sean M Carroll (who says he thinks it's 50/50 but certainly doesnt believe inflation solves the low entropy initial condition question).
But I have seen so many papers online of people who seems to think inflation can somehow explain the low entropy initial condition. Surely for that to be the case it would have to be an adiabatic process which I don't see how it can be especially when it 'ends' and fills the universe with particles, surely this is an entropy raising process?  If you have read Huw Price and understand his argument (and believe it, which I think you have to as I don't see any logical flaw) then any natural initial conditions must also be natural end conditions, making deflation just as likely as inflation yet noone talks about that possibility.  And if deflation is not possible, then surely the only explanation for this is because inflation raised entropy and deflation would decrease it, hence inflation cannot provide an answer as to why the universes initial conditions were so special?
Mostly I'd like to get the view of people who DO think inflation explains the low entropy past, and have them tell me how they refute Huw Price's argument?
 A: Inflation as a whole is an entropic process, but one has to distinguish between the two phases of inflation.
First you have the slow roll regime where the Universe is vacuum-dominated and expands exponentially. This is where the massive increase in size comes into play, and where the horizon and flatness problems of Big Bang cosmology are resolved. It's called a slow roll because the matter field that is thought to drive inflation (conventionally some scalar field $\phi$ called the inflaton) is "rolling down" a vacuum energy potential which for this regime is extremely flat. The equation of motion will be:
\begin{equation}
\ddot{\phi} + 3H\dot{\phi} + \Gamma _{\phi} \dot{\phi} = - \frac{dV(\phi)}{d\phi}
\end{equation}
where $H = \dot{a}/a$ is the Hubble parameter/rate of expansion, $\Gamma _{\phi}$ is the decay width of the inflaton into other particle species, and $V(\phi)$ is the potential. The spatial derivatives and other terms inversely proportional to the scale factor $a$ are neglected, since they become minuscule very quickly.
To ensure the flatness of the potential, this comes down to the two slow roll parameters:
\begin{equation}
\begin{split}
\varepsilon &= -\frac{\dot{H}}{H^{2}} \\
\eta &= -\frac{\ddot{\phi}}{\dot{\phi}H}
\end{split}
\end{equation}
Both of these have to approach 0 for the slow roll conditions to be met.
After the slow roll regime concludes, the inflaton field "slides down" towards the absolute minimum of the potential and the Universe transitions into a matter-dominated phase, since the inflaton quanta now will start behaving like massive, non-relativistic particles. But due to the massive drop in vacuum energy, the inflaton field acquires a great amount of kinetic energy, so in reality the Universe quickly then becomes radiation-dominated. This is called the reheating phase. The inflaton field will rapidly oscillate about the minimum, and due to the fact it is expected to be coupled to other forms of matter, it decays constantly into other particles. This is where most of the entropy of the observable Universe comes from.
An example of an inflationary potential that follows this paradigm is something like this:

$\phi _{i}$ is the starting value of the inflaton field when the slow roll begins, $\phi _{e}$ its value upon exiting the slow roll regime, and $\sigma$ is its value where the minimum of the potential is located. Here I juxtapose the roll of the inflaton with an analogous classical equivalent, which is a ball rolling down a hill with friction. In the case of inflation, it's the rate of expansion $H$ and the decay width $\Gamma _{\phi}$ that play the role of friction.
Since conventional Big Bang cosmology commences after the reheating phase, the low entropy that is predicted so that our current observations are consistent can be handily met due to reheating, based on the particular model at hand and the e-folds (duration) of the slow roll regime. This of course means the Universe prior to the slow roll begins at a state of even lower entropy, but that is not contrary to observation, unlike the estimated low entropy of the Big Bang model which runs contrary to the CMBR mesurements. In other words, the low entropy problem is only a major problem in the Big Bang cosmological model; for inflation this is a matter of an open question as to why the initial state of even lower entropy occurred, as opposed to equilibrium initial conditions.
The objection to inflation as a solution to this problem is therefore due to some physicists such as Sean Carroll finding the low entropy initial condition "unnatural", and thus the explanation incomplete. There are arguments which are reasonable for that proposal, but fundamentally there is nothing inherently wrong or problematic with the initial conditions that inflationary models presuppose. The major open question is to justify them.
