Ph.D. Dissertation Defense: Yunlong Huang Tuesday, July 25, 2017
2:00 p.m. 2168 AVW Bldg.
For More Information: Maria Hoo 301 405 3681 mch@umd.edu

ANNOUNCEMENT: Ph.D. Dissertation Defense

Name: Yunlong Huang

Committee:

Professor P.S. Krishnaprasad, Chair

Professor Steve. Marcus

Professor Andre Tits

Professor Jonathan M. Rosenberg

Professor Christopher Jarzynski, Dean's Representative

Date/Time: Tuesday July 25, 2017 at 2:00 pm

Place: 2168 AVW

Title: Optimal control of heat engines in non-equilibrium statistical mechanics

Abstract:

A heat engine is a cyclically operated statistical mechanical systems which converts heat supply from a heat bath into mechanical work. As it is operated in finite time, this non-equilibrium statistical mechanical system is a dissipative system. In this dissertation, our research focuses on two heat engines: one is a stochastic oscillator and the other is a capacitor connected to a Nyquist-Johnson resistor (a stochastically driven resistor-capacitor circuit). These two heat engines are parametrically-controlled. A path in the parameter space of a heat engine is designated as a protocol.

In the first chapter of this dissertation, under the near-equilibrium assumption, with the help of linear response theory, fluctuation theorem and stochastic thermodynamics, we consider an inverse diffusion tensor in the parameter space of a heat engine. The inverse diffusion tensor of the stochastic oscillator induces a hyperbolic space structure in the parameter space composed of the stiffness of the potential well and the inverse temperature of the heat bath. The inverse diffusion tensor of the resistor-capacitor circuit induces an Euclidean space structure in the parameter space composed of the capacitance of the capacitor and the inverse temperature of the heat bath. The average dissipation rate of a heat engine is given by a quadratic form (with a positive-definite inverse diffusion tensor) on the tangent space of the system parameter.

Along a finite-time protocol of a heat engine, besides the energy dissipation, there are two auxiliary quantities: one is the extracted work of the heat engine and the other is the total heat supply from the bath to the engine. These two quantities are fundamental to the analysis of the efficiency of a heat engine. Combining the energy dissipation and the extracted work of a heat engine, we introduce sub-Riemannian geometry structures underlying both heat engines in Chapter 2.

In Chapter 3, with the definition of efficiency of a heat engine, we show the equivalence between an optimal control problem in the sub-Riemannian geometry of the heat engine and the problem of maximizing the efficiency of the heat engine. In this way, we bring geometric control theory to non-equilibrium statistical mechanics. In particular, we explicate the relation between conjugate point theory and the working loops of a heat engine. As a related calculation, we solve the isoperimetric problem in hyperbolic space as an optimal control problem in Chapter 4.

Based on the theoretical analysis in the first four chapters, in the final chapter of the dissertation, we adopt level set methods, mid-point approximation and shooting method to design the maximum-efficiency working loops of both heat engines. The associated efficiencies of these protocols are computed.

Based on the theoretical analysis in the first four chapters, in the final chapter of the dissertation, we adopt level set methods, mid-point approximation and shooting method to design the maximum-efficiency working loops of both heat engines. The associated efficiencies of these protocols are computed.