Quantum work in the Bohmian framework
Physical Review A
American Physical Society
©2018 American Physical Society
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system’s initial conditions and its interaction with the environment. The fluctuating work, for example, is characterised by the ensemble of system trajectories in phase space and, by including the probabilities for various trajectories to occur, a work distribution can be constructed. However, without phase space trajectories, the task of constructing a work probability distribution in the quantum regime has proven elusive. Here we use quantum trajectories in phase space and define fluctuating work as power integrated along the trajectories, in complete analogy to classical statistical physics. The resulting work probability distribution is valid for any quantum evolution, including cases with coherences in the energy basis. We demonstrate the quantum work probability distribution and its properties with an exactly solvable example of a driven quantum harmonic oscillator. An important feature of the work distribution is its dependence on the initial statistical mixture of pure states, which is reflected in higher moments of the work. The proposed approach introduces a fundamentally different perspective on quantum thermodynamics, allowing full thermodynamic characterisation of the dynamics of quantum systems, including the measurement process.
This work has been in part supported by the Academy of Finland through its CoE grants 284621 and 287750. R.S. acknowledges support from the Magnus Ehrnrooth Foundation. J.A. acknowledges support from EPSRC (grant EP/M009165/1) and the Royal Society. This research was supported by the COST network MP1209 “Thermodynamics in the quantum regime”.
This is the author accepted manuscript. The final version is available from American Physical Society via the DOI in this record.
Vol. 97(1), 012131.