Active Brownian heat engines

When do nonequilibrium forms of disordered energy qualify as heat? We address this question in the context of cyclically operating heat engines feeding on nonequilibrium energy reservoirs that defy the zeroth law of thermodynamics into work. To consistently address a nonequilibrium bath as a heat bath in the sense of the second law of thermodynamics requires the existence of a precise mapping to an equivalent cycle with an equilibrium bath at a time-dependent effective temperature. We identify the most general setup for which this can generically be ascertained and thoroughly discuss an analytically tractable, experimentally relevant scenario: a Brownian particle confined in a periodically modulated harmonic potential and coupled to some nonequilibrium bath of variable activity. We deduce formal limitations for its thermodynamic performance, including maximum efficiency, efficiency at maximum power, and maximum efficiency at fixed power. The results can guide the design of new micromachines and clarify how much these can outperform passive-bath designs, which has been a debated issue for recent experimental realizations. To illustrate the practical implications of the general principles for quasistatic and finite-rate protocols, we further analyze a specific realization of such an active heat engine based on the paradigmatic active Brownian particle (ABP) model. This reveals some nonintuitive features of the explicitly computed dynamical effective temperature, illustrates various conceptual and practical limitations of the effective-equilibrium mapping, and clarifies the operational relevance of various coarse-grained measures of dissipation.