THERMODYNAMICS AT THE NANOSCALE: CLASSICAL AND QUANTUM SYSTEMS

Abstract

Work is one of the most basic notions in statistical mechanics, with work fluctuation theorems being one central topic in nanoscale thermodynamics. Here we present general salient results regarding how (classical) Hamiltonian chaos generically impacts on nonequilibrium work fluctuations. For isolated chaotic systems prepared at an initial microcanonical or canonical distribution at inverse temperature β, work fluctuations in form of Var(W) or exponential work fluctuations depicted by the variance of e-βW are minimized by adiabatic work protocols. This general result indicates that, if Var(e-βW) diverges for an adiabatic work protocol, it diverges for all nonadiabatic work protocols sharing the same initial and final Hamiltonians. Such divergence is hence not an isolated event and thus greatly impacts on the efficiency of using the Jarzynski’s equality to simulate free energy differences. Theoretical results are illustrated in a Sinai model. Similar phenomena are reproduced in quantum systems. We further propose g-deformed work Wg to eliminate Var(e-βWg). The corresponding deformed fluctuation theorems are also proposed. Our general insights shall boost studies in nanoscale thermodynamics and are of fundamental importance in designing useful work protocols and engine cycles.