Stochastic dynamics and fluctuation theorems in Brownian, feedback-controlled, and optical cavity systems

This thesis investigates stochastic dynamics in a range of classical systems, with a focus on fluctuation theorems and the physical interpretation of the quantities entering these relations. It begins with an investigation of the added mass effect in harmonically coupled underdamped Brownian particles. A measurement time interval is incorporated into the model to explicitly account for finite temporal resolution in experimental conditions. Exact expressions for the effective mass, as well as approximate expressions obtained under timescale separation, are derived. These results demonstrate that the added mass effect arises from insufficient temporal resolution to resolve all relevant velocity fluctuations. Next, continuous measurement and feedback in an overdamped Brownian particle system are analyzed. Fluctuation theorems and second-law-like inequalities are derived for entropy production associated with both the system variable and the feedback parameter, and these results are interpreted in terms of information flow. A solvable harmonic feedback model is subsequently analyzed and mapped to an equivalent autonomous system, providing a thermodynamic interpretation of the derived quantities and relations. Furthermore, fluctuation theorems in optical cavity dynamics are examined. In particular, fluctuation theorems are derived for quantities analogous to total entropy production, housekeeping heat, and non-autonomous work in coherently driven nonlinear optical cavity systems. In the linear regime, analytical expressions for these quantities are obtained. In addition, a mapping between the linear optical cavity and an overdamped Brownian particle subject to a harmonic potential and rotational drift is established. Together, these results clarify the roles of system parameters and external protocols in generating irreversibility in the cavity dynamics. Finally, a hierarchy of alternating inequalities for the truncated cumulant expansion of entropy production in homogeneous Markov jump processes is presented. While this result is not central to the main theme of the thesis, it reveals a simple yet nontrivial mathematical structure underlying such processes. The systems studied in this thesis are diverse, including Brownian particles, feedback-controlled systems, optical cavities, and Markov jump processes; each chapter is largely self-contained. Taken together, these results show how stochastic dynamics can be used to characterize fluctuations and irreversibility, and to derive effective quantities as well as constraints on entropy production in classical systems with a small number of degrees of freedom.

Department dc:contributor.department

Physics

Year dc:date.issued

2026

Author dc:creator

• CHEUNG, Long Him

Advisor dc:contributor.advisor

• Jarzynski, Christopher

Language dc:language.iso

en

Identifier

https://doi.org/10.13016/cseo-dzce

OAI identifier oai:identifier

oai:drum.lib.umd.edu:1903/35902