Control and optimisation of irreversible processes in non-equilibrium systems

TL;DR

This thesis explores controlling non-equilibrium stochastic systems, focusing on memory effects, glassy behavior, and optimizing state transitions by manipulating temperature and potential parameters.

Contribution

It introduces new insights into memory effects and optimal control strategies in non-equilibrium systems within statistical mechanics.

Findings

Memory effects and glassy behavior linked to non-equilibrium attractors.

Optimal protocols for minimizing transition times by tuning temperature and stiffness.

Analysis of non-equilibrium attractors in thermal bath systems.

Abstract

This thesis is devoted to the study of physical systems embedded within the field of non-equilibrium statistical mechanics. Specifically, the state of the systems of interest constitutes a stochastic process that can be externally driven by a set of controllable parameters. On the one hand, for systems in contact with a thermal bath, we have studied the emergence of strong memory effects and glassy behaviour upon varying the bath temperature, and how these are related to the existence of non-equilibrium attractors governing the dynamics. On the other hand, for overdamped harmonic systems, we have studied the problem of minimising the connection time between arbitrary stationary (either equilibrium or non-equilibrium) states, by suitably varying either the bath temperature or the stiffnesses of the potential.