Energy Harvesting from Anisotropic Temperature Fields

Harvesting energy stands as a fundamental trait of living organisms. Yet, relevant processes rarely conform to the setting of Carnot’s engine alternating contact between heat baths of different temperatures. Instead, fluctuations and anisotropic chemical concentrations seem to provide the source of cellular energy. In this chapter, we explore how to (optimally) harvest energy from anisotropic fluctuations. Specifically, we consider an overdamped system in which the different degrees of freedom are in contact with different temperature heat baths, and maximize work extraction by periodic potential control. We show that path-lengths traversed in the manifold of thermodynamic states, measured in a suitable Riemannian metric (the Wasserstein-2 metric), represent dissipative losses, while area integrals of a work-density quantify work being extracted. Thus, the maximal amount of work that can be extracted relates to an isoperimetric problem, trading off area against length of an encircling path. Moreover, we derive an isoperimetric inequality that provides a universal bound on the efficiency of all cyclically operating protocols, and a bound on the speed with which a closed path can be traversed before it becomes impossible to extract positive work.