The multivariate fluctuation relation is established for the full counting statistics of the energy and particle fluxes across an open quantum system in contact with several reservoirs on the basis of microreversibility The quantum version of the nonequilibrium work fluctuation relation is recovered in the presence of a single reservoir. In the long-time limit, the time-reversal symmetry relation is expressed in terms of the cumulative generating function for the full counting statistics. In systems with independent particles, the symmetry relation can be obtained in the scattering approach for the transport of bosons and fermions. The temporal disorder and its time asymmetry can be characterized by the quantum version of the entropy and coentropy per unit time. Their difference gives the thermodynamic entropy production rate. Furthermore, the stochastic approach is also considered for electron transport in quantum dots, quantum point contacts, and single-electron transistors.

1. Introduce density distribution and momentum distribution of non-interacting Fermi gas.

2. Discuss the transport property of a Fermi gas through a quantum point contact.

3. Discuss Fermi surface as a key of a non-interacting Fermi gas and its generalization to a Fermi liquid.

4. Introduce the effective mass and the quasi-particle residue as two key parameters of the Fermi liquid.

5. Introduce the self-energy and the universal relations between the effective mass, the quasi-particle residue and the self-energy.

6. Discuss Fermi polaron as an example of the Fermi liquid, and show these universal relations with this example.

7. Discuss the divergence of the effective mass and vanishing of quasi-particle residue when Fermi liquid description fails.

8. Introduce the radio-frequency spectroscopy and how it measures the polaron energy and the quasi-particle residue.

9. Summarize different spectroscopy measurements in ultracold atomic systems.