  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.
