Optimal control of dissipation and work fluctuations for rapidly driven systems

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.

Analytical solution for optimal protocols of weak drivings

“…showing that the irreversible work is a non-null constant, as expected by a rapidly-driven protocol where the sudden change in the parameter irreversibly dissipates energy [17,18]. Observe also that such optimal irreversible work is the same as the one calculated in [11] considering only jumps at the beginning and end of the process.…”

“…Using the symmetric property (18) in the second term of the left-hand side of equation ( 19), one has…”

“…Therefore, studying particular examples or building numerical procedures seems to be a better course than finding a general aspect that unifies analytically this phenomenon in this particular regime [14][15][16]. Notorious exceptions however have been found in the context of rapidly driven systems [17,18], and geometric thermodynamics applied to Fokker-Planck formalism [19].…”