Do low interest rates cause deflation?

Schmidt and Woodford are working this problem.

Let's do currency flow first, then price distortion second.

We have no idea what low is. Let me give you the version of this problem from the theory of everything.

If the stable growth of deposits minus the stable growth of loans is less than one than the currency banker is draining money from the economy to the recycle bin. Stable growth means the two period growth as in the hyperbolic condition.

Why use this method?
Because equipartition is guaranteed and we get both fermion and boson statistics.  That is the fundamental basis of self adapting statistics. We can also say this is the input-output queueing model.

Intertemporal optimization does not work because term periods and rates  are outputs, not inputs.  Sorry economists, you have always gotten this wrong. For example, we do not know what rates and terms were until we settle accounts and derive the implicit price deflator.

Put this in layman's terms.  If the currency banker does not 'lose' enough ink and paper to cover growth then we get deflation.

Price distortion:
 When government, by law, encourages a doubling of emergency room visits in a quarter then you get price distortion and crash.

I had thought we had gone beyond the simple Euler assumption, but I guess economists continue to fall back on the simple minded math.  Remember, the new model adjusts adaptation variance to stability, and kinetic motion of institutions and transactions conform to that minimization.  That is why California does this, constantly:

Figure out why we have this motion and you will have a complete theory of economics.  Here is a clue, this motion is what is necessary to maintain a balance between the encode and decode process, using Shannon information theory.

Using the hyperbolic, two period model the issue is allocating the second derivative of the growth to decay ratios so all transactions are maximum entropy.  This is different from the original Shannon model, which assumed a fixed channel rate. The channel rate is adapted to the nearest precision maintainable, and that means motion is guaranteed, by equipartition. Another name for it is two sided Black-Scholes. This is also the theory behind banker bot, by the way. . Beyond that, go hire a mathematician.