Nonequilibrium thermodynamics with binary quantum correlations

The balance equations for thermodynamic quantities are derived from the nonlocal quantum kinetic equation. The nonlocal collisions lead to molecular contributions to the observables and currents. The corresponding correlated parts of the observables are found to be given by the rate to form a molecule multiplied with its lifetime which can be considered as collision duration. Explicit expressions of these molecular contributions are given in terms of the scattering phase shifts. The two-particle form of the entropy is derived extending the Landau quasiparticle picture by two-particle molecular contributions. There is a continuous exchange of correlation and kinetic energies condensing into the rate of correlated variables for energy and momentum. For the entropy, an explicit gain remains and Boltzmann's H theorem is proved including the molecular parts of the entropy.

Figure 1

Displacements in the effective collision of real particles. In the scattering-out process, the momenta $k$ and $p$ correspond to the initial states of particles $a$ and $b$, the momenta $k-q$ and $p+q$ to the final states. In the scattering-in process, the picture is reversed.

Figure 2

Transformation A as interchange of particle $a$ and $b$ leading to (10).

Figure 3

Transformation B as interchange of incoming and outgoing particles leading to (15).