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Shortcut to isothermality is a driving strategy to steer the system to itsequilibrium states within finite time, and enables evaluating the impact of acontrol promptly. Finding optimal scheme to minimize the energy cost is ofcritical importance in applications of this strategy in pharmaceutical drugtest, biological selection, and quantum computation. We prove the equivalencebetween designing the optimal scheme and finding the geodesic path in the spaceof control parameters. Such equivalence allows a systematic and universalapproach to find the optimal control to reduce the energy cost. We demonstratethe current method with examples of a Brownian particle trapped in controllableharmonic potentials.

Geodesic path for the minimal energy cost in shortcuts to isothermality