Is a physical process with unbounded input Turing equivalent? Church-Turing thesis states that any effectively computable process is computable by a TM. Let's assume for now that it means that every physical machine is computable by a TM. Let's call it A. 

Now if this process has an unbounded number of states (for example we could think of an engine in a car and take the geographic coordinates of the car as its states) we could say that A is also Turing complete.

And therefore Turing equivalent.

Edit: Let's try to see more precisely how A could be considered as Turing complete even if the physical is continuous. Let's for example consider a car moved by an engine. And let's consider a planet where towns' names are built with the classic alphabet A, B, C etc. following rules that make the number of towns on that planet potentially infinite or unbounded. Now let's imagine that my vehicle is programmed by an algorithm to drive from town to town indefinitely. Let's call these towns the states of my system. Now I am certain (but please correct me if I am wrong) that my physical system is indeed Turing complete - and not just a push down automaton. Now if you accept that any state an observer (typically a physicist) will use to describe a physical system can be coded in a finite alphabet i.e. an integer (even if the physical world is continuous) then surely we could use the vehicle experience to say that in human eyes the physical world is Turing complete. 

Is that correct?
No.  You can't just sweep everything under the rug like that.  The answer depends on what model of reality / physics you subscribe to.

If your model of reality is continuous (e.g., Newtonian physics), then it's not necessarily true that that every physical machine is computable by a TM.  TM's are discrete, not continuous; if physics is actually continuous, then your assumption is probably not correct.  (It might be true that the outcome of a process can be computed to an arbitrary degree of accuracy by a TM, but that's a subtly different statement.  TM's compute discrete values, not continuous values.)

If your model of reality is discrete and finite, then it might be true that that every physical machine is computable by a TM.  But now the number of states is not unbounded.

You can't have it both ways.  Or, to put it another way, you can't just assume things without justification.