Geometry of Finite-Time Thermodynamic Cycles With Anisotropic Thermal Fluctuations

In contrast to the classical concept of a Carnot engine that alternates contact between heat baths of different temperatures, naturally occurring processes usually harvest energy from anisotropy, being exposed simultaneously to chemical and thermal fluctuations of different intensities. In these cases, the enabling mechanism responsible for transduction of energy is typically the presence of a non-equilibrium steady state (NESS). A suitable stochastic model for such a phenomenon is the Brownian gyrator – a two-degree of freedom stochastically driven system that exchanges energy and heat with the environment. In the context of such a model we present, from a stochastic control perspective, a geometric view of the energy harvesting mechanism that entails a forced periodic trajectory of the system state on the thermodynamic manifold. Dissipation and work output are expressed accordingly as path integrals of a controlled process, and fundamental limitations on power and efficiency are expressed in geometric terms via a relationship to an isoperimetric problem. The theory is presented for high-order systems far from equilibrium and beyond the linear response regime.