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.
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The Arrow of Time  »The Arrow of Time 
The experience of time »The experience of time
Passage view components »Passage view components
Flow and direction of time? »Flow and direction of time?
Memory accretion hypothesis  »Memory accretion hypothesis 
Direction is that of memory accretion »Direction is that of memory accretion
Why aligned with thermodynamic arrow? »Why aligned with thermodynamic arrow?
Information theoretic explanation
Argument from computation »Argument from computation
Quantum argument »Quantum argument
Causality, not entropy »Causality, not entropy
Refrigerator objection »Refrigerator objection
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