Abstract
A central topic in the emerging field of quantum thermodynamics is the definition of thermodynamic work in the quantum regime. One widely used solution is to define work for a closed system undergoing non-equilibrium dynamics according to the two-point energy measurement scheme. However, due to the invasive nature of measurement the two-point quantum work probability distribution cannot describe the statistics of energy change from the perspective of the system alone. We here introduce the quantum histories framework as a method to characterise the thermodynamic properties of the unmeasured, closed dynamics. Constructing continuous power operator trajectories allows us to derive an alternative quantum work distribution for closed quantum dynamics that fulfils energy conservation and is time-reversal symmetric. This opens the possibility to compare the measured work with the unmeasured work, contrasting with the classical situation where measurement does not affect the work statistics. We find that the work distribution of the unmeasured dynamics leads to deviations from the classical Jarzynski equality and can have negative values highlighting distinctly non-classical features of quantum work.
Highlights
Einstein’s enquiry to Bohr if ‘the Moon does not exist if nobody is looking at it’ questions the indeterminate nature of a quantum state when it is not measured [1]
We find that the resulting work distribution is a quasi-probability distribution, implying that for general closed quantum dynamics fluctuating work cannot be interpreted as a measurable system property, while moments of the work distribution are well-defined and measurable
While in classical thermodynamics the act of measurement leaves no influence on the statistical properties of the system, in quantum mechanics one faces a dilemma: either one measures the fluctuating work and accepts disturbing the system, or one does not disturb the system but there is no data to read off the fluctuating work value
Summary
Commons Attribution 3.0 work in the quantum regime. One widely used solution is to define work for a closed system licence. Constructing continuous power operator trajectories allows us to derive an alternative quantum work distribution for closed quantum dynamics that fulfils energy conservation and is time-reversal symmetric. This opens the possibility to compare the measured work with the unmeasured work, contrasting with the classical situation where measurement does not affect the work statistics. We find that the work distribution of the unmeasured dynamics leads to deviations from the classical Jarzynski equality and can have negative values highlighting distinctly non-classical features of quantum work
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have