Shortcuts to state transitions for active matter

TL;DR

This paper develops a geometric shortcut framework for swift state transitions in active matter systems, minimizing dissipation by following geodesic paths in control parameter space.

Contribution

It introduces a thermodynamic metric and geodesic-based optimal protocols for finite-time control of active systems in the weak activity regime.

Findings

Geodesic protocols reduce dissipation compared to linear protocols.

The framework applies to active systems with external traps and internal interactions.

An approximate auxiliary potential is used when exact derivation is infeasible.

Abstract

Shortcut schemes can accelerate quasi-static processes in passive systems by adding auxiliary controls to realize swift transitions between equilibrium states. In active systems, however, inherently directed motion driven by free energy consumption continually drives the system away from equilibrium. In this work, we develop a shortcut framework to realize swift state transitions for active systems operating in the weak activity regime. An auxiliary potential is introduced to guide the system along a predefined distribution path, allowing it to reach the target state within a finite time. Considering unavoidable energy cost in such a finite-time process, we derive a thermodynamic metric from the dissipative work to induce a Riemann manifold on the space spanned by the control parameters. The optimal protocol with minimum dissipative work is then identical to the geodesic path in the geometric space. We demonstrate this framework by considering active systems confined in an external harmonic trap and interacting via two distinct internal potentials, respectively: an attractive harmonic coupling and a repulsive pairwise Gaussian-core coupling. The strengths of both the external trap and the internal interactions are controllable. For the latter case, since the auxiliary potential can not be derived precisely, we adopt a variational method to obtain an approximate auxiliary control. Compared to linear protocols, the geodesic protocols can effectively reduce dissipation.