  The autonomous heat engine is a model system of autonomous nonequilibrium
systems like biological cells, exploiting nonequilibrium flow for operations.
As the Carnot engine has essentially contributed to the equilibrium
thermodynamics, autonomous heat engine is expected to play a critical role in
the challenge of constructing nonequilibrium thermodynamics. However, the high
complexity of the engine involving an intricate coupling among heat, gas flow,
and mechanics has prevented simple modeling. Here, we experimentally
characterized the nonequilibrium dynamics and thermodynamics of a
low-temperature-differential Stirling engine, which is a model autonomous heat
engine. Our experiments demonstrated that the core engine dynamics are
quantitatively described by a minimal dynamical model with only two degrees of
freedom. The model proposes a novel concept that illustrates the engine as a
thermodynamic pendulum driven by a thermodynamic force. This work will open a
new approach to explore the nonequilibrium thermodynamics of autonomous systems
based on a simple dynamical system.
