Efficiency fluctuations in microscopic machines

Abstract

Nanoscale machines are strongly influenced by thermal fluctuations, contrary to their macroscopic counterparts. As a consequence, even the efficiency of such microscopic machines becomes a fluctuating random variable. Using geometric properties and the fluctuation theorem for the total entropy production, a `universal theory of efficiency fluctuations' at long times, for machines with a finite state space, was developed in [Verley \textit{et al.}, Nat.~Commun.~\textbf{5}, 4721 (2014); Phys.~Rev.~E~\textbf{90}, 052145 (2014)]. We extend this theory to machines with an arbitrary state space. Thereby, we work out more detailed prerequisites for the `universal features' and explain under which circumstances deviations can occur. We also illustrate our findings with exact results for two non-trivial models of colloidal engines.

12 pages, 6 Figures; version published in the journal

References in corpus (15)

• The large deviation approach to statistical mechanics
• The unlikely Carnot efficiency
• Path-integral analysis of fluctuation theorems for general Langevin processes
• Extended Heat-Fluctuation Theorems for a System with Deterministic and Stochastic Forces
• The Brownian gyrator: a minimal heat engine on the nano-scale
• Efficiency statistics at all times: Carnot limit at finite power
• Experimental Realization of a Minimal Microscopic Heat Engine
• Universal theory of efficiency fluctuations
• Efficiency fluctuations in quantum thermoelectric devices
• Efficiency and Large Deviations in Time-Asymmetric Stochastic Heat Engines
• Unifying approach for fluctuation theorems from joint probability distributions
• Work fluctuations for a Brownian particle in a harmonic trap with fluctuating locations
• Stochastic Efficiency for Effusion as a Thermal Engine
• Stochastic Efficiency: Five Case Studies
• Asymptotics of work distributions in a stochastically driven system