Operational definition of many-body dynamical activity

Determine how to associate dynamical activity, and thereby frenesy, with large collections of interacting particles in an experimentally and operationally meaningful way, including within nonequilibrium field theories and for geometric degrees of freedom.

Background

The paper states that the operational use of frenesy becomes problematic as the number of degrees of freedom grows. Although a system may be reduced to a smaller set of fluctuating collective variables, interactions among many microscopic degrees of freedom eventually become relevant, making the direct characterization of activity potentially overwhelming.

The authors suggest that nonequilibrium field theories may provide a route by replacing explicit many-body structure with nonlinearities, but describe this replacement as challenging. They further connect the problem to steady-state thermodynamics, active surfaces and membranes, and the need for a dynamical fluctuation theory for geometric degrees of freedom, where the nature of geometric dynamical activity remains to be clarified.