Past is a conceptual construct that only seems solid in the absence of careful examination. But if you look closely you will see that Past is assembled by the mind from multiple cues (as is Present by the way).
The minuteexperience of second-to-minutesecond flow of time is a byproduct of chitta-vrtti, the associative cycle, when each subsequent dharma (~thought) comes by association with the previous one. The sense of relatedness of the two dharmas is what creates the illusion of flow.
Disclaimer: this answer represents my own experience and understanding and is not meant to reflect an official position or to be consistent with views of any Buddhist school.