Title:

The Impossible Quantum Work Distribution

Abstract:

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. 
Indeed, the existence of such a distribution based on generalised 
measurements has recently been ruled out 
[Phys. Rev. Lett. 118, 070601 (2017)]. 
In the talk I will present a fresh perspective on the issue based on 
Bohmian trajectories and the quantum Hamilton-Jacobi equation 
[Sampaio, R. et al., arXiv:1708.05113 [quant-ph]]. 
In complete analogy to classical physics, work is naturally defined 
as power integrated along phase space trajectories. 
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 the 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 and it thus goes beyond the 
framework of generalised measurements. The proposed approach allows the 
full thermodynamic characterisation of the dynamics of quantum systems, 
including the measurement process.