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Stochastic thermodynamics has revolutionized our understanding of heatengines operating in finite time. Recently, numerous studies have consideredthe optimal operation of thermodynamic cycles acting as heat engines with agiven profile in thermodynamic space (e.g. $P-V$ space in classicalthermodynamics), with a particular focus on the Carnot engine. In this work, weuse the lens of thermodynamic geometry to explore the full space ofthermodynamic cycles with continuously-varying bath temperature in search ofoptimally shaped cycles acting in the slow-driving regime. We apply classicalisoperimetric inequalities to derive a universal geometric bound on theefficiency of any irreversible thermodynamic cycle and explicitly constructefficient heat engines operating in finite time that nearly saturate this boundfor a specific model system. Given the bound, these optimal cycles perform moreefficiently than all other thermodynamic cycles operating as heat engines infinite time, including notable cycles, such as those of Carnot, Stirling, andOtto. For example, in comparison to recent experiments, this corresponds toorders of magnitude improvement in the efficiency of engines operating incertain time regimes. Our results suggest novel design principles for futuremesoscopic heat engines and are ripe for experimental investigation.

A geometric bound on the efficiency of irreversible thermodynamic cycles