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Summary

Optimal protocols for finite-time transitions in controllable systems minimize mean work. Including inertia, delta-peak changes in control parameters at boundaries optimize the process, enhancing free energy calculations.

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Area of Science:

Statistical mechanics
Non-equilibrium thermodynamics
Physical chemistry

Background:

Systems in controllable potentials transition between equilibrium states.
Optimal protocols minimize mean work for finite-time transitions.
Overdamped dynamics suggest boundary jumps in control parameters.

Purpose of the Study:

Investigate optimal protocols for systems with inertia.
Determine the impact of inertia on optimal control parameters.
Enhance free energy calculations using insights from optimal protocols.

Main Methods:

Analysis of systems with time-dependent potentials.
Inclusion of inertia terms in dynamic equations.
Study of paradigmatic cases: Brownian particle in optical traps.

Main Results:

Optimal protocols persist with boundary delta-peak changes in control parameters when inertia is included.
Inertia does not alter the necessity of boundary control parameter adjustments.
Demonstrated optimality of delta-peak-like changes at process boundaries.

Conclusions:

Inertia inclusion reinforces the importance of boundary control parameter changes for optimal protocols.
Findings can improve free energy calculations using thermodynamic integration or Jarzynski's equality.
Optimal control strategies are crucial for efficient non-equilibrium processes.