On the irreversibility of collective motion in polar active matter

Abstract

• Chapter 1 – Introduction to the contents and main results of the thesis. • Chapter 2 – Review of Itô and Stratonovich calculus, stochastic thermodynamics, (stochastic) entropy production, time-reversal symmetry, the principle of detailed balance, Sekimoto’s stochastic energetics and spherical diffusions, with example applications. • Chapter 3 – Review of the Vicsek model (VM), the ‘continuous-time Vicsek model’ (CTVM) and mean-field theory of the CTVM. This chapter also includes some unpublished results on the stability of the polar liquid phase of the CTVM in mean-field, in addition to the coarse-grained hydrodynamic theory of the CTVM. The work done in this chapter has been done under the supervision of Michael E. Cates. • Chapter 4 – Unpublished analytical and numerical results on the ‘Active XY model’ (AXYM), including a linear stability analysis of the polar liquid phase of the AXYM and ‘non-extensive AXYM’ (NeAXYM). This work has been done under the supervision of Michael E. Cates. Sections 4.4 and 4.6 contain numerical investigations and a linear stability analysis of the coarse-grained hydrodynamic theory of the AXYM in d = 2, which has been published in paper 1. in the publications section, and has been done under the supervision of Michael E. Cates and Étienne Fodor. • Chapter 5 – Unpublished results on the construction of the entropy production rate (EPR) in the CTVM, AXYM and NeAXYM, in addition to both numerical and analytical investigations of the EPR at high densities. The work in this chapter has been done under the supervision of Michael E. Cates and Étienne Fodor. • Chapter 6 – Numerical and analytical investigation of the EPR in two hydrodynamic theories of polar active matter; the hydrodynamic Vicsek model (HVM) and diffusive flocking model (DFM). The relationship between the scaling of the EPR with noise intensity and violation of time-reversal symmetry is investigated. The work in this chapter has been published in paper 1. in the publications section, and has been done under the supervision of Michael E. Cates and Étienne Fodor. • Chapter 7 – Concluding remarks and summary the main findings in the thesis, including reflections and an outlook on potential future directions. Throughout the thesis, all figures and tables have either been prepared for the dissertation or are taken from paper 1. in the publications section where not explicitly stated otherwise.