, Volume 31, Issue 4, pp 743-785

Memory systems, computation, and the second law of thermodynamics

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Abstract

A memory is a physical system for transferring information from one moment in time to another, where that information concerns something external to the system itself. This paper argues on information-theoretic and statistical mechanical grounds that useful memories must be of one of two types, exemplified by memory in abstract computer programs and by memory in photographs. Photograph-type memories work by exploiting a collapse of state space flow to an attractor state. (This attractor state is the “initialized” state of the memory.) The central assumption of the theory of reversible computation tells us that inany such collapsing, regardless of whether the collapsing proceeds from the past to the future or vice versa, the collapsing must increase the entropy of the system. In concert with the second law, this establishes the logical necessity of the empirical observation that photograph-type memories are temporally asymmetric (they can tell us about the past but not about the future). Under the assumption that human memory is a photograph-type memory, this result also explains why we humans can remember only our past and not our future. In contrast to photograph-type memories, computer-type memories do not require any initialization, and therefore are not directly affected by the second law. As a result, computer memories can be of the future as easily as of the past, even if the program running on the computer is logically irreversible. This is entirely in accord with the well-known temporal reversibility of the process of computation. This paper ends by arguing that the asymmetry of the psychological arrow of time is a direct consequence of the asymmetry of human memory. With the rest of this paper, this explains, explicitly and rigorously, why the psychological and thermodynamic arrows of time are correlated with one another.