Impact of emergent order on energy efficiency in active matter: Insights from a minimal lattice model

Abstract

We investigate the nonequilibrium steady state of a one-dimensional (i.e., mechanical degree of freedom) run-and-tumble model of left-right oriented Brownian particles with an explicit coupling to a chemical degree of freedom and a macroscopic opposing force. This model enables us to explore the fundamental relationships between the energy process driving individual entities, the emergence of collective behavior, and macroscopic forces in active matter. Sufficiently large alignment interactions can break the right-left symmetry, leading to a macroscopic collective alignment of the particles, or flocking transition. Using a decoupling mean-field approximation, we find that collective alignment requires both sufficiently large alignment interactions and lattice hopping. Further, this collective alignment does not require chemical-to-mechanical coupling and can occur solely through passive mechanical hopping. If chemical-to-mechanical coupling is present, it can lead to a collective drift in the direction of particle alignment even against an opposing mechanical force. Interestingly, in the absence of an opposing force, the particles spontaneously align in a random direction, but in the presence of a force, they tend to align “uphill,” enabling macroscopic work output. The many-body system is formulated in terms of creation and annihilation operators for identical classical particles, which enables us to calculate a range of observables by exploiting techniques from many-body quantum systems.