Even though the change of energy and the related concepts of heat and work are fundamental quantities in thermodynamics, their understanding in the context of quantum systems is still incomplete. Here, 'work' W is commonly defined as energy transfer during some deformation of the system. It requires a two-time measurement scheme, in which the energy E of the time evolved system is measured at time t=0, and at a later time t. Work is thus a statistical quantity due to thermal and quantum fluctuations. 

We study[1] the full distribution of quantum work in generic, noninteracting, disordered fermionic nanosystems at finite temperature. In particular, we consider disordered zero-dimensional quantum dots described by Random Matrix Theory in which we derive an analytical determinant formula for the characteristic function of work statistics for quantum quenches starting from a thermal initial state. For work small compared to the thermal energy of the Fermi gas, work distribution is Gaussian, and the variance of work is proportional to the average work, while in the low-temperature or large-work limit, a non-Gaussian distribution with superdiffusive work fluctuations is observed. Similarly, the time dependence of the probability of adiabaticity crosses over from an exponential to a stretched exponential behavior. For large enough average work, the work distribution becomes universal, and depends only on the temperature and the mean work. Apart from initial low-temperature transients, work statistics are well captured by a Markovian energy-space diffusion process of hardcore particles, starting from a thermal initial state. Our findings can be verified by measurements on nanoscale circuits or via single qubit interferometry

[1]: A Grabarits, M Kormos, I Lovas, and G Zaránd, Phys. Rev. B 106, 064201 (2022)