Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping

Abstract

We propose a method to study the thermodynamic behaviour of small systems\nbeyond the weak coupling and Markovian approximation, which is different in\nspirit from conventional approaches. The idea is to redefine the system and\nenvironment such that the effective, redefined system is again coupled weakly\nto Markovian residual baths and thus, allows to derive a consistent\nthermodynamic framework for this new system-environment partition. To achieve\nthis goal we make use of the reaction coordinate mapping, which is a general\nmethod in the sense that it can be applied to an arbitrary (quantum or\nclassical and even time-dependent) system coupled linearly to an arbitrary\nnumber of harmonic oscillator reservoirs. The core of the method relies on an\nappropriate identification of a part of the environment (the reaction\ncoordinate), which is subsequently included as a part of the system. We\ndemonstrate the power of this concept by showing that non-Markovian effects can\nsignificantly enhance the steady state efficiency of a three-level-maser heat\nengine, even in the regime of weak system-bath coupling. Furthermore, we show\nfor a single electron transistor coupled to vibrations that our method allows\none to justify master equations derived in a polaron transformed reference\nframe.\n