Nonequilibrium dynamics and thermodynamics of some single particle activity induced diffusive systems

Abstract

In the mesoscopic world, diffusion is a ubiquitous process and it is usually explained by the Einstein s theory of Brownian motion (BM). However, in the biological systems, some peculiar dynamical behaviors are observed as opposed to those of the BM [1,2]. Such characteristics can be understood by considering that apart from the thermal noise, the system is subjected to an additional noise called active noise stemming from some active processes such as ATP hydrolysis. Due to the presence of active noise, the system is driven out of equilibrium as it is manifested by the breakdown of the conventional fluctuation-dissipation relation (FDR). In the first part of my thesis (Chapter 1- 5), we study two activity-induced diffusive systems - (i) self-propelled particle and (ii) passive colloidal particle in the active surroundings [3]. The dynamics of a self-propelled particle is conceived through the run-and-tumble particle (RTP) model in which the active noise is taken as dichotomous (telegraphic) noise. By employing the phasespace path integral (PSPI) technique, we find that unlike free Brownian motion, the distributions at early and intermediate times are double-peaked, as has been observed experimentally [4]. On confining them in a harmonic potential, the distribution is often found to be concentrated near the boundaries. This is the trait of RTPs such as bacteria, Janus particles, as supported by many theoretical calculations and experimental evidences [5]. Another problem we deal with is the diffusive motion of a passive particle in a bath containing active particles such as bacteria, motor proteins, etc. By modelling the active bath by Gaussian colored noise (GCN), we find that the distribution is always Gaussian with an enhanced diffusivity. Similar traits have been observed in the diffusion processes of colloids in a low-dense bacterial solution [1, 6]...