Optimization of Stochastic Heat Engines in the Underdamped Limit 1st Edition by Nikolas Zölle 3658163501 9783658163501

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ISBN-10 :  3658163501 

ISBN-13 :  9783658163501

Author:  Nikolas Zölle 

Nikolas Zöller examines the working principles and the underlying theoretical foundations of a microscopic heat engine. In particular, he investigates the system’s stochastic dynamics in the underdamped regime which has hardly been studied in the past, but will be experimentally feasible in the near future due to recent technological developments. Emphasis is put on the maximization of the engine’s efficiency at maximum power through optimization of the driving protocol. In addition, possible experimental realizations of a microscopic heat engine are discussed.

Optimization of Stochastic Heat Engines in the Underdamped Limit 1st Table of contents:

1 Introduction
1.1 Stochastic Dynamics
1.1.1 Langevin Equation
1.1.2 Fokker-Planck Equation
1.1.3 Wiener Process
1.1.4 Stochastic Differential Equations (SDE)
1.1.5 High-Friction Limit
1.2 Stochastic Energetics
1.2.1 Thermodynamics of Single Trajectories
1.2.2 Ensemble Averages
1.3 Classical Heat Engines
1.3.1 Carnot Engine
1.3.2 Curzon-Ahlborn Engine
2 Stochastic Heat Engine – Overdamped Regime
2.1 Carnot-type Model of a Stochastic Heat Engine
2.2 Optimal Protocols in the Overdamped Limit for an Harmonic Trapping Potential
2.3 Breakdown of the Overdamped Limit
2.3.1 Motivation
2.3.2 Numerical Study
3 Experimental Setups in Overdamped and Underdamped Regimes
3.1 Realization of a Stirling Engine in a Colloidal System
3.2 Optical Cavity Trap
3.2.1 Effective Heat Engine via Optical Damping
3.2.2 Numerical Study
4 Stochastic Heat Engine – Underdamped Regime
4.1 Optimization Problem
4.2 Low Friction Approximation
4.3 Explicit Protocols
4.3.1 Simple Linear Protocol
4.3.2 Piecewise Linear Protocol
5 Entropy Production in Inhomogeneous Thermal Environments
5.1 Entropic Anomaly
5.2 Case Study – Quadratic Temperature Profile
5.3 Entropy Production in Optical Trap Setup
6 Conclusions and Outlook

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Tags: Optimization, Stochastic, Heat Engines, Underdamped, Nikolas Zölle