Perspective: The Physics of Active Solids -- From Hamiltonians to Active Matter Models

Abstract

The physics of active matter, wherein constituent particles consume energy to generate autonomous motion, has revolutionized non-equilibrium statistical mechanics. While a large body of work has successfully elucidated the behavior of dilute active systems, the dense regime -- characterized by ``active glasses and active solids'' -- presents profound challenges that defy conventional theoretical frameworks. Recent observations reveal two striking features in these dense systems: an apparent enhancement of Mermin-Wagner-Hohenberg (MWH) fluctuations leading to anomalous long-wavelength density fluctuations, and a remarkable correspondence between activity-induced annealing and annealing via oscillatory shear. In this perspective article, we propose a novel approach toward a deeper understanding of dense active matter: by developing active Hamiltonian models as equilibrium reference frameworks, we map out pathways toward non-equilibrium active systems. This strategy allows us to elucidate both the correspondence between driven and active systems and the enhanced MWH fluctuations, which likely arise from a strong coupling between spatially random active forces and long-wavelength density (phonon) modes. We outline a comprehensive roadmap employing complementary approaches, including the active Hamiltonian formalism, comparative studies of oscillatory shear in active and passive solids, and investigations of chiral active matter. Establishing this activity-oscillatory shear correspondence across diverse systems is essential to demonstrate its universality, reveal the underlying large-scale emergent physics, and place our hypothesis on a firmer theoretical ground.