  Accurate information processing is crucial both in technology and in nature.
To achieve it, any information processing system needs an initial supply of
resources away from thermal equilibrium. Here we establish a fundamental limit
on the accuracy achievable with a given amount of nonequilibrium resources. The
limit applies to arbitrary information processing tasks and arbitrary
information processing systems subject to the laws of quantum mechanics. It is
easily computable and is expressed in terms of an entropic quantity, which we
name reverse entropy, associated to a time reversal of the information
processing task under consideration. The limit is achievable for all
deterministic classical computations and for all their quantum extensions. As
an application, we establish the optimal tradeoff between nonequilibrium and
accuracy for the fundamental tasks of storing, transmitting, cloning, and
erasing information. Our results set a target for the design of new devices
approaching the ultimate efficiency limit, and provide a framework for
demonstrating thermodynamical advantages of quantum devices over their
classical counterparts.
