Entropy production of active particles formulated for underdamped dynamics
Derek Frydel
Abstract
The present work investigates the effect of inertia on the entropy production rate $\mathrm{\ensuremath{\Pi}}$ for all canonical models of active particles for different dimensions and the type of confinement. To calculate $\mathrm{\ensuremath{\Pi}}$, the link between the entropy production and dissipation of heat rate is explored, resulting in a simple and intuitive expression. By analyzing the Kramers equation, alternative formulations of $\mathrm{\ensuremath{\Pi}}$ are obtained and the virial theorem for active particles is derived. Exact results are obtained for particles in an unconfined environment and in a harmonic trap. In both cases, $\mathrm{\ensuremath{\Pi}}$ is independent of temperature. For the case of a harmonic trap, $\mathrm{\ensuremath{\Pi}}$ attains a maximal value for $\ensuremath{\tau}={\ensuremath{\omega}}^{\ensuremath{-}1}$, where $\ensuremath{\tau}$ is the persistence time and $\ensuremath{\omega}$ is the natural frequency of an oscillator. For active particles in one-dimensional box, or other nonharmonic potentials, thermal fluctuations are found to reduce $\mathrm{\ensuremath{\Pi}}$.