John, Thank you! That's great. I will read your review of Zeh and the Chapter I online of Price. And quite possibly buy one or both.
The deadline is May 1. But I'm thinking that I should apply. Because I do have a novel perspective. Basically my novel ideas are that:
A) The issue of "deciding" necessitates a framework given by "the division of everything into five perspectives": Every effect has had its cause, but not every cause has had its effects. And the boundary/present is where these two causal directions coincide. This framework, cognitively, has two representations: we imagine it either as time (cause in past, effect in future) or space (cause outside a subsystem, effect inside a subsystem). More about the "divisions of everything" here: http://www.ms.lt/derlius/20170220LevelsOfKnowledge.pdf
B) Cognitively, our emotional lives are driven by expectations, especially the temporal boundary between expecting and learning an outcome, and the spatial boundary between self and world. I write about that here: http://www.ms.lt/sodas/Book/TaxonomyOfMoods
C) Intuitively, think of entropy in terms of "deliberateness" and "nondeliberateness". Googling on "entropy deliberateness" doesn't yield much, so perhaps that's novel.
D) The role of the coordinate system - who decides the particular coordinate system used? - because whoever decides can scramble and unscramble the "phase space" at will.
E) A particular set of atoms, say, may seem meaninglessly chosen. And yet if we study what happens to those atoms - their flow through the system - then we may nevertheless witness signs of life. So the definition of life - for example - as that which can have ("(self)-interest") - is related to entropy. A frog has "self-interest" directly, and a clock (which has a potential owner) has "(self)-interest" on behalf of its owner. Which is to say, life is that which we can be helped or hurt. (In Lithuanian, we have a word "nauda" ("what is useful to us"), which suggest that something can be done on our behalf. And I'm thinking, you can't do anything on behalf of something that's not alive, but only for that which is alive - to whatever degree.)
F) Entropy, as I wrote above, is important in discussing the ambiguity of open systems (based on grace) and closed systems (based on justice). Yes, locally, at a certain level, we're fueled by the Sun, and yet again, at bigger and smaller levels things are crumbling all the same. So the ambiguity seems very important.
G) Prayer is (if it is anything) a way of engineering, of increasing the likelihoods of miracles. I think it does this by increasing the ambiguity required for (God or external forces) to intervene (without breaking any laws too badly). So explaining this dynamics would be my main idea.
These are not the usual ideas. But maybe that's what they are possibly looking for. It's certainly helpful for me to think about.
I appreciate any links to the above ideas (supporting or rejecting) with perspectives in math and physics. Thank you!