Derivations of master equations using projection operator methodology are based upon an identity whose validity has been established in only limited contexts. Its proof requires precise definitions of eLt and , where L is the Liouville operator and P the projection operator associated with the limited system information of interest. Here, for interacting particles confined to a box, the existence and uniqueness of system dynamics is demonstrated. A distributional extension of L defined in an L1 space is derived for which is the corresponding updating operator. Attempts to define within current semigroup theory are outlined, and a possible future approach indicated.
|Number of pages||18|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Publication status||Published - 3 Aug 2001|
- liouville operator
- projection operator
- semigroup theory
Lamb, W., Murdoch, I., & Stewart, J. (2001). On an operator identity central to projection operator methodology. Physica A: Statistical Mechanics and its Applications, 298(1), 121-139. https://doi.org/10.1016/S0378-4371(01)00214-X