Entropy production of active particles in underdamped regime

The present work investigates the effect of inertia on the entropy production rate $\Pi$ for all canonical models of active particles, for different dimensions and the type of confinement. To calculate $\Pi$, the link between the entropy production and dissipation of heat rate is explored. By analyzing the Kramers equation in a stationary state, alternative formulations of $\Pi$ 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, $\Pi$ is independent of temperature. In contrast, for active particles in 1D box, thermal fluctuations are found to reduce $\Pi$

Run-and-tumble oscillator: moment analysis of stationary distributions

When it comes to active particles, even an ideal-gas model in a harmonic potential poses a mathematical challenge. An exception is a run-and-tumble model (RTP) in one-dimension for which a stationary distribution is known exactly. The case of two-dimensions is more complex but the solution is possible. Incidentally, in both dimensions the stationary distributions correspond to a beta function. In three-dimensions, a stationary distribution is not known but simulations indicate that it does not have a beta function form. The current work focuses on the three-dimensional RTP model in a harmonic trap. The main result of this study is the derivation of the recurrence relation for generating moments of a stationary distribution. These moments are then used to recover a stationary distribution using the Fourier-Lagrange expansion

Thermodynamic collapse in a lattice-gas model for a two-component system of penetrable particles

We study a lattice-gas model of penetrable particles on a square-lattice substrate with same-site and nearestneighbor interactions. Penetrability implies that the number of particles occupying a single lattice site is unlimited and the model itself is intended as a simple representation of penetrable particles encountered in realistic soft-matter systems. Our specific focus is on a binary mixture, where particles of the same species repel and those of the opposite species attract each other. As a consequence of penetrability and the unlimited occupation of each site, the system exhibits thermodynamic collapse, which in simulations is manifested by an emergence of extremely dense clusters scattered throughout the system with energy of a cluster E ∝ −n2, where n is the number of particles in a cluster. After transforming a particle system into a spin system, in the large density limit the Hamiltonian recovers a simple harmonic form, resulting in the discrete Gaussian model used in the past to model the roughening transition of interfaces. For finite densities, due to the presence of a nonharmonic term, the system is approximated using a variational Gaussian model