Optimal control of dissipation and work fluctuations for rapidly driven systems

TL;DR

This paper identifies optimal control protocols for rapidly driven classical and quantum systems that minimize dissipation and work fluctuations, featuring two discontinuous jumps in control variables, with applications to quantum systems, bit erasure, and Ising chains.

Contribution

It characterizes the structure of optimal driving protocols in fast regimes, revealing they involve two jumps and can interpolate or minimize dissipation and fluctuations simultaneously.

Findings

Optimal protocols involve two discontinuous jumps in control variables.

Protocols can interpolate between minimal dissipation and minimal fluctuations.

Applications demonstrated in quantum systems, bit erasure, and Ising chains.

Abstract

To achieve efficient and reliable control of microscopic systems one should look for driving protocols that mitigate both the average dissipation and stochastic fluctuations in work. This is especially important in fast driving regimes in which the system is driven far out of equilibrium, potentially creating large amounts of unwanted entropy production. Here we characterise these optimal protocols in rapidly driven classical and quantum systems and prove that they consist of two discontinuous jumps in the full set of control variables. These jumps can be tuned to interpolate between processes with either minimal dissipation or minimal fluctuations, and in some situations allow for simultaneous minimisation. We illustrate our general results with rapidly driven closed quantum systems, classical bit erasure and a dissipative Ising chain driven close to a quantum phase transition.