Information theoretic explanation
A number of physicists and philosophers have claimed that remembering - by humans or computers - can only occur in a rising-entropy environment. Such claims generally draw on the requirements for persisting and utilizing information. Two approaches to formally demonstrating this link are addressed.
In addition a number of physicists and philosophers have simply asserted that the psychological (memory) arrow must align with the thermodynamic arrow - see citations below from Sean Carroll and J.J.C. Smart.