  One of the major resource requirements of computers - ranging from biological
cells to human brains to high-performance (engineered) computers - is the
energy used to run them. Those costs of performing a computation have long been
a focus of research in physics, going back to the early work of Landauer. One
of the most prominent aspects of computers is that they are inherently
nonequilibrium systems. However, the early research was done when
nonequilibrium statistical physics was in its infancy, which meant the work was
formulated in terms of equilibrium statistical physics. Since then there have
been major breakthroughs in nonequilibrium statistical physics, which are
allowing us to investigate the myriad aspects of the relationship between
statistical physics and computation, extending well beyond the issue of how
much work is required to erase a bit. In this paper I review some of this
recent work on the `stochastic thermodynamics of computation'. After reviewing
the salient parts of information theory, computer science theory, and
stochastic thermodynamics, I summarize what has been learned about the entropic
costs of performing a broad range of computations, extending from bit erasure
to loop-free circuits to logically reversible circuits to information ratchets
to Turing machines. These results reveal new, challenging engineering problems
for how to design computers to have minimal thermodynamic costs. They also
allow us to start to combine computer science theory and stochastic
thermodynamics at a foundational level, thereby expanding both.
