Statistical Physics: Transport Theory

The methods used are:

• Irreversible Thermodynamics

  General symmetries and the Second Law of Thermodynamics as well as particular ansätze for the Free Energy are used to derive phenomenological equations and to generalise thermo-hydrodynamics.

• Analytical and Numerical Solutions

  of the phenomenological equations for particular geometries in order to allow comparison with experiment.

• Kinetic Theory

  Application of kinetic equations for one- and two-particle distribution functions, e.g.

  • Boltzmann Equation for the velocity distribution
  • Kirkwood-Smoluchowski Equation for the pair correlation functions
  • Fokker-Planck Equation for the orientation distribution function
  Derivation and application of generalisations of these equations.

• Molecular Dynamics Computer Simulation

  A many-body theory in which only the microscopic interaction of the particles and certain constraints, such as temperature, are specified. In analogy to experimental measurements, the quantities of interest are extracted from the simulation according to the rules of statistical mechanics. Equilibrium and non-equilibrium properties such as transport and relaxation processes may be investigated within the framework of of MD und NEMD (NonEquilibrium Molecular Dynamics) computer simulations. Fast processes and states far from thermal equilibrium are also accessible via this type of analysis.