Thermodynamics of Minimal Coupling Quantum Heat Engines

Abstract

The Minimal Coupling Quantum Heat Engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which couples alternatively to subsystems through discrete steps -energy conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a process of the work extraction is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed through a flow of passive energy. Our main result is finding the optimal efficiency and work extracted per cycle of the three-stroke engine with the two-level working body. We reveal that small dimensionality of the working body and a restriction to two-body operations make the engine fundamentally irreversible, such that efficiency is always less than Carnot or extracted work is always less than free energy. In addition, we propose a generalization of many-stroke engine, and in particular we analyze efficiency vs extracted work trade-offs, as well as work fluctuations after many cycles of running of the engine. One of key new tools is the introduced "control-marginal state" -one which acts only on a working body Hilbert space, but encapsulates all the features of total working body-battery system regarding work extraction. For the special cases (e.g. total state being diagonal in energy eigenbasis) the above state reduces to the standard marginal state, although, in general, these two states are distinct, which is a signature of coherences or entanglement between the working body and the battery.

All states are universal catalysts in quantum thermodynamics

“…We begin by describing the resource theory of quantum thermodynamics. As a starting point we define a restricted set of quantum operations known as thermal operations (TO's) which were introduced in [22], and subsequently studied in [11,21,[45][46][47][48][49][50][51][52][53][54][55][56][57]. This is an established setting which allows for exploring fundamental thermodynamic limitations by assuming perfect control over the environment.…”