  A thermal current, generated by a temperature gradient between two reservoirs
coupled to a carefully designed photonic or (micro-) electromechanical circuit,
might induce non-conservative forces that impulse a mechanical degree of
freedom to move along a closed trajectory. We show that in the limit of long -
but finite - modulation periods, the extracted power and the efficiency of such
autonomous motors can be maximized when an appropriately designed
spatio-temporal symmetry violation is induced and when the motor operates in
the vicinity of exceptional point (EP) degeneracies. These singularities appear
in the spectrum of the effective non-Hermitian Hamiltonian that describes the
combined circuit-reservoirs system when we judiciously tailor the coupling
between them. In the photonic framework, these motors can be propelled by
thermal radiation and can be utilized as autonomous self-powered microrobots,
or as micro-pumps for microfluidics in biological environments. The same
designs can be also implemented with electromechanical elements for harvesting
ambient mechanical (or electrical) noise for powering a variety of auxiliary
systems.
