Quantum fluctuation theorems and power measurements

Abstract

Workinthe paradigm of the quantum fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energyat the beginning and end of the force protocol. Inanalogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating upthe resultsofrepeated measurements ofthe instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). Inthe limitofmany projective measurementsofpower, the system's dynamics isfrozen in the power measurement basis due tothe quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relationis not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of powerbased definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurementsofpower are considered within the stochastic master equation formalism. Eveninthis scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics.