Stochastic Thermodynamics of Small Systems: Inference, Irreversibility and Information

Das, Biswajit (2025) Stochastic Thermodynamics of Small Systems: Inference, Irreversibility and Information. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Biswajit Das (18IP005)) 18IP005.pdf - Submitted Version Restricted to Repository staff only Download (19MB)

Abstract

Thermal fluctuations dominate the dynamics of mesoscopic systems, resulting in the stochastic nature of processes occurring at the mesoscale. Such noisy systems often remain out of equilibrium as they evolve through a sequence of states shaped by internal interactions, the surrounding environment, and external controls or feedback mechanisms, with energy potentially dissipated at each step. This thesis explores the thermodynamic aspects of mesoscopic nonequilibrium processes in the presence of various interactions and complex environments within the framework of stochastic thermodynamics. In this context, the entropy production rate serves as a central thermodynamic parameter, as its non-zero value quantifies how far a system is from equilibrium. While theoretical prescriptions for calculating entropy production under known dynamics are well established, extracting it from experimental or numerical trajectories without full knowledge of the dynamics remains challenging. In the first part of this thesis, we establish and validate an indirect method to estimate the entropy production rate using experimental or numerical trajectories of microscopic systems. The short-time inference technique, which is agnostic to the details of the underlying dynamics, provides a powerful tool to investigate nonequilibrium behavior in complex systems (both linear and nonlinear) especially where analytical calculations are intractable. As an application, we numerically explore the Brownian gyrator in anharmonic potentials, where entropy production cannot be computed analytically due to the underlying nonlinear dynamics. We then study entropy currents in overdamped nonequilibrium systems governed by linear and nonlinear Langevin dynamics. An experimentally realized optically trapped colloidal system perturbed with correlated noise serves as an example of linear dynamics, while anharmonic Brownian gyrators represent nonlinear cases. In both systems, the skewness of the time-integrated entropy currents exhibits a nonmonotonic dependence on the integration time, revealing rich signatures of the underlying nonequilibrium conditions. Next, we proceed to examine the aspects of nonequilibrium processes in the presence of interactions. Hydrodynamic interactions – ubiquitous in liquid environments – introduce intriguing dynamical effects when colloidal particles are trapped in close proximity. However, their role in affecting the overall irreversibility of such systems if they are taken out of equilibrium remains fairly less explored. In this context, we consider a system of two optically trapped colloids held in close separation, with one of them driven by exponentially correlated noise. By estimating entropy production, we show that nonequilibrium features depend strongly on the level of coarse-graining. Specifically, we show that increasing the interaction strength by reducing the distance between the particles lowers the total irreversibility of the full system. However, when focusing on a coarse-grained subspace that includes only the particles (excluding the external drive), the trend reverses: the measured irreversibility increases with interaction strength. To interpret this apparent paradox related to coarse-graining and irreversibility, we employ information-theoretic measures such as mutual information and its time-delayed variants, which reveal how irreversibility is distributed across different phase planes of an interacting system. Finally, we examine the impact of memory effects, or time-delayed responses of the medium, by studying active processes in viscoelastic environments, realized experimentally with optical tweezers. Compared to purely viscous baths, viscoelastic surroundings enhance the mean input power and suppress negative work fluctuations, highlighting how non-Markovianity fundamentally reshapes energetics. Even at identical levels of activity,the nature of fluctuations differs entirely between viscoelastic and viscous environments. In summary, this thesis presents a comprehensive account of mesoscopic nonequilibrium processes, emphasising the roles of fluctuations, interactions, and memory in shaping entropy production and irreversibility. The combination of stochastic energetics with inference and information-theoretic approaches not only offers versatile tools for studying complex nonequilibrium systems but also lays the groundwork for designing controlled thermodynamic protocols in the future.

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