  A non-vanishing entropy production rate is one of the defining
characteristics of any non-equilibrium system, and several techniques exist to
determine this quantity directly from experimental data. The short-time
inference scheme, derived from the thermodynamic uncertainty relation, is a
recent addition to the list of these techniques. Here we apply this scheme to
quantify the entropy production rate in a class of microscopic heat engine
models called Brownian gyrators. In particular, we consider models with
anharmonic confining potentials. In these cases, the dynamical equations are
indelibly non-linear, and the exact dependences of the entropy production rate
on the model parameters are unknown. Our results demonstrate that the
short-time inference scheme can efficiently determine these dependencies from a
moderate amount of trajectory data. Furthermore, the results show that the
non-equilibrium properties of the gyrator model with anharmonic confining
potentials are considerably different from its harmonic counterpart -
especially in set-ups leading to a non-equilibrium dynamics and the resulting
gyration patterns.
