Molecular identification and chromosomal localization of new powdery mildew resistance gene Pm11 in oat

Work in the paradigmof the quantumfluctuation theorems of Crooks and Jarzynski is determined by projectivemeasurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeatedmeasurements of the 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 thework determined by the conventional two energymeasurement approach (TEMA). In the limit ofmany projective measurements of power, the system’s dynamics is frozen in the powermeasurement basis due to the quantumZeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the casewhen the instantaneous power operator commutes with the totalHamiltonian at all times.We also consider properties of the joint statistics of powerbased definition of work andTEMAwork in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projectivemeasurement condition, weak continuous measurements of power are consideredwithin the stochasticmaster equation formalism. Even in this scenario the power-basedwork statistics is in general not able to reproduce qualitative features of the TEMAwork statistics.