Estimating the energetics along a fluctuating trajectory of an active particle

Active matter is a specific type of matter with constituents that consume energy to exert mechanical forces. Such systems are intrinsically out of thermal equilibrium and have characteristics that are not well understood. In equilibrium systems, the thermal energy is dissipated as described by the fluctuation-dissipation theorem. Likewise, an active system must also dissipate the input energy to remain in a steady state; however, in contrast to thermal forces, active fluctuations are likely non-Gaussian, strongly dependent upon frequency, and with an amplitude proportional to the specific characteristics of the active system. On average, these characteristics are well-defined; however, their stochastic fluctuations with time are less understood. We seek to estimate the energetics of dissipation along a stochastic trajectory of an active particle. To this end, we study the inertial Langevin equation, since the commonly-used overdamped approximation yields diverging results for a particle's path energetics. We use a combined numerical and analytical approach to estimate fluctuating properties along a trajectory and then compare the results to experimental measurements.