Energy Harvesting in a 2-dimensional Anisotropic Temperature field

We consider overdamped Brownian particles with two degrees of freedom (DoF), confined in a time-varying quadratic potential and subject to anisotropic fluctuations. We quantify maximal work extraction via an isoperimetric problem where the Wasserstein length of cyclic trajectory quantifies dissipation and a surface integral over the enclosing curve in the manifold of thermodynamic states (thermodynamic cycle) quantifies extracted work. The efficiency can likewise be bounded by an isoperimetric inequality, providing universal speed limits to work extraction. The analyis extends earlier results that pertain to the case where the entropy of thermodynamic states is kept constant along the cycle. Our present analysis, that addresses the general case, shows that by exploring variation in entropy dissipation along the cycle can be reduced, as compared to the constant-entropy case. Thereby, we characterize optimal trajectories that attain maximal work output and efficiency in complete generality.