Alladi Ramakrishnan Hall

Modeling of Stochasticity on Geometric Brownian Information

Syed Yunus Ali

IIT Tirupati

Our research focuses on the fundamentals of stochastic thermodynamics and how it connects to the information (surprisal) related to microscopic particles inside a fluctuating environment and subjected to an entropic potential. When Brownian particles are spatially confined inside a narrow channel with an irregular shape, they feel an effective entropic potential as a function of the local phase space of the confinement along the direction of their transport. We first explore a thorough understanding of how an unbiased driving force manifests a response in the system in terms of the work done and the absorbed heat when a Brownian particle is confined inside a bilobal irregular structure. Other major objective of the present thesis involves the construction of a Brownian Information Engine (BIE) in the presence of an entropic potential and how the physical properties of such an engine change with the geometric restrictions. Therefore, the primary goals of the present research are twofold:
1. To study a few aspects of the stochastic thermodynamics of a Brownian particle confined inside an irregular geometric enclosure.
2. To design Geometric Brownian Information Engines (GBIE) with appropriate feedback protocols and, hence, to explore the conditions for best performances.
The study begins by considering the motion of an overdamped Brownian particle inside a 2-D bilobal confinement. Apart from the thermal fluctuations, particles experience periodic external driving along the longitudinal direction and a constant bias force (G) along the perpendicular transverse coordinate. By tuning the value of G, the effective entropic potential can be changed from an entropy-dominated to an energy-dominated one. The intention of this study is to figure out how the nonlinearity of the effective entropic potential, which results from the unevenness of the confinement, impacts the thermodynamic responses. We calculate thermodynamic responses as the work done and heat absorbed by the system. We identify the condition (parameter space) when a constructive interplay between thermal noise, external driving, and effective entropic potential leads to a nontrivial response in terms of nonzero work done. A frequency matching situation between the time scales of inter-lobal escape and the cycle time of external periodic driving has been identified that contributes to producing most efficient response. The study also establishes the possibility of quantifying entropic stochastic resonance (ESR) phenomena using these thermodynamic observables.
Next, we construct a Geometric Brownian Information Engine (GBIE) considering the constrained motion of a Brownian particle inside a 2-D monolobal confinement. The setup is subjected to an appropriate feedback cycle that consists measurement, feedback and relaxation process. The study aims to ascertain the upper bound of achievable work and how it varies when entropic control is raised. Our research also looks for the optimal requirements for the maximum extractable work and the favorable conditions in which the device functions as an engine. Several time-dependent observables, such as

power and efficiency, were also evaluated to study the conditions for extracting the maximum work change over the cycle time. We explain the observed results/conditions in terms of the available information acquired during such feedback protocol. Overall, this thesis contributes to understanding stochastic thermodynamics and its connection with information in confined systems. It provides insights into the design principle and efficiency of a Geometric Brownian information engine and their potential applications in various domains.