  Heat engines and information engines have each historically served as
motivating examples for the development of thermodynamics. While these two
types of systems are typically thought of as two separate kinds of machines,
recent empirical studies of specific systems have hinted at possible
connections between the two. Inspired by molecular machines in the cellular
environment, which in many cases have separate components in contact with
distinct sources of fluctuations, we study bipartite heat engines. We show that
a bipartite heat engine can only produce net output work by acting as an
information engine. Conversely, information engines can only extract more work
than the work consumed to power them if they have access to different sources
of fluctuations, i.e., act as heat engines. We illustrate these findings first
through an analogy to economics and a cyclically controlled 2D ideal gas. We
then explore two analytically tractable model systems in more detail: a
Brownian-gyrator heat engine which we show can be reinterpreted as a
feedback-cooling information engine, and a quantum-dot information engine which
can be reinterpreted as a thermoelectric heat engine. Our results suggest
design principles for both heat engines and information engines at the
nanoscale, and ultimately imply constraints on how free-energy transduction is
carried out in biological molecular machines.
