33 research outputs found
Entropy production of active particles in underdamped regime
The present work investigates the effect of inertia on the entropy production
rate for all canonical models of active particles, for different
dimensions and the type of confinement. To calculate , 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
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, is independent of temperature. In contrast,
for active particles in 1D box, thermal fluctuations are found to reduce
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