Read-once machines and the thermodynamic complexity of Maxwell's demons

Abstract

The thermodynamical costs imposed by computational resource limitations like memory and time have been investigated before. We focus on a new computational limitation, namely, the machine being allowed to scan the input only once, and prove that it is associated with unavoidable thermodynamical cost, even in the presence of infinite time and memory resources. We identify this limitation to be the one suffered by Maxwell's demons. This provides a framework for quantifying the complexity associated with an experiment that effectuates a "decrease" in the entropy of a thermodynamic system.