Abetract. Governing equations of molectiar simulations that involve coupling between molecular and macroscopie proplerties are derived from z linetic equation.
Keywords. Molecular simulatzans, kinetic theory.
INTRODUCTION
In molecular simulations a macroscopic system is regarded as composed of n representative particles. Trajectories of the garticles are calculated on a computer. The following questions arjse:
(i) What are the equations that qovern the time evolution of the representative particles; how they differ fron the equations that qovern the time evolution of the molecules composing the system under consideration?
(ii) How the macroscopic information of interest (i.e. the information that we are receivina as a result of observations and measurements of the system under considerationl is extracted from the trajectories of the n representative particles?
(iii) How the macroecopie constraints ased in our sbservations and control uf the system under consideration are expressed in terms of the particle characterizations and how they intluence the time evalution of the representative particles?
For recent reviews of simulation scteres see Refs, 1,2 .
Dur objective in this paper is to shom that the problem of answering the above three questions is closely related to the problem of formulating n"particle kinetic equations, simulation schemes are derived form the kinetic equations. In fact, a simulation scheme can be regarded as a method of solving numerically a n-particle kinetic equation. This observation is useful since it allows to "se the physical insight that has been collected in nonequilibrium statistical mechanics, in particular ther in kiretic theory, to formulate appropriate simulation schwnes. Conversely, the pbseryation made if this paper offers also a new way to use molacular sifulations for adwahcing neriequilibrium statistical mechanics. As an illustratign. we derive from a kinetic equation an extension of the Nose-Hoover scheme for isothernal simulations.