Coupled and Hidden Degrees of Freedom in Stochastic Thermodynamics

TL;DR

This thesis explores the interactions of coupled and hidden degrees of freedom in stochastic thermodynamics, emphasizing the role of information, reversibility, and hidden variables in energy dissipation and entropy production.

Contribution

It develops a framework for analyzing entropy production in interacting and hidden systems, integrating information theory with stochastic thermodynamics.

Findings

Reversible interactions are necessary for thermalization.

Hidden variables can significantly underestimate energy dissipation.

Bounds on hidden entropy production can be derived from partial observations.

Abstract

This thesis investigates the interactions of different degrees of freedom of one joint system within the theory of stochastic thermodynamics. First, a comprehensive introduction to the subjects of stochastic processes, information theory and the theory of stochastic thermodynamics is given, thereby highlighting the key results. In the second part, systems with interacting degrees of freedom are considered. This allows investigation of thermalization properties of collisional baths, i.e. particles at equilibrium interacting with a localized system via collisions. It is shown that the interactions between system and bath must be reversible to ensure thermalization of the system. Moreover, the role of information in thermodynamics is presented and interpreted in the context of interacting systems. Using the concept of causal conditioning, a framework is developed for finding entropy productions that capture the mutual influence of coupled subsystems. This framework is applied to diverse setups which are usually studied separately in information thermodynamics. The third part covers the case of important system variables being hidden from observation. The problem is motivated by presenting a microswimmer model and showing that its movement can be approximated by active Brownian motion. However, its energy dissipation is massively underestimated by this procedure. It is shown that this is a consequence of the fact that the swimming mechanism is a hidden variable. Subsequently, different methods of effective description are discussed and applied to a simple model system with which the impact of hidden slow degrees of freedom on fluctuation theorems is studied. Finally, a setting is investigated in which it is possible to give bounds for the hidden entropy production from only partial observation of the system dynamics by fitting an underlying hidden Markov process to the observable data.