Free power dissipation from functional line integration

Abstract

Power functional theory provides an exact generalisation of equilibrium density functional theory to non-equilibrium systems undergoing Brownian many-body dynamics. Practical implementation of this variational approach demands knowledge of an excess (over ideal gas) dissipation functional. Using functional line integration (i.e. the operation inverse to functional differentiation), we obtain an exact expression for the excess free power dissipation, which involves the pair interaction potential and the two-body, equal-time density correlator. This provides a basis for the development of approximation schemes.

Keywords:

• density functional theory
• dynamical density functional theory
• liquid state structure
• Brownian dynamics
• perturbation theory

PACS numbers:

• 61.20.Gy
• 64.10.+h
• 05.20.Jj

Acknowledgements

It is a great pleasure to dedicate this paper to Jean-Pierre Hansen, whose work has shaped our thinking about physics in many useful ways.

Disclosure statement

No potential conflict of interest was reported by the authors.