  We consider overdamped Brownian particles with two degrees of freedom (DoF)
that are confined in a time-varying quadratic potential and are in simultaneous
contact with heat baths of different temperatures along the respective DoF. The
anisotropy in thermal fluctuations can be used to extract work by suitably
manipulating the confining potential. The question of what the maximal amount
of work that can be extracted is has been raised in recent work, and has been
computed under the simplifying assumption that the entropy of the distribution
of particles (thermodynamic states) remains constant throughout a thermodynamic
cycle. Indeed, it was shown that the maximal amount of work that can be
extracted amounts to solving an isoperimetric problem, where the 2-Wasserstein
length traversed by thermodynamic states quantifies dissipation that can be
traded off against an area integral that quantifies work drawn out of the
thermal anisotropy. Here, we remove the simplifying assumption on constancy of
entropy. We show that the work drawn can be computed similarly to the case
where the entropy is kept constant while the dissipation can be reduced by
suitably tilting the thermodynamic cycle in a thermodynamic space with one
additional dimension. Optimal cycles can be locally approximated by solutions
to an isoperimetric problem in a tilted lower-dimensional subspace.
