Canonical equilibrium, dynamic approach

This observation reinforces, rather than weakens, the importance of the result of Ref. 84 insofar as it shows that with merely dynamic arguments the authors of this paper did derive the appropriate form of Boltzmann principle. This result sets the challenge for the derivation of the thermodynamic properties of Levy statistics from the same dynamic approach as that used in Ref. 84 to derive canonical equilibrium. 

The present article presents an introduction to the path integral formulation of quantum dynamics and quantum statistical mechanics along with numerical procedures useful in these areas and in electronic structure theory. Section 2 describes the path integral formulation of the quantum mechanical propagator and its relation to the more conventional Schrddinger description. That section also derives the classical limit and discusses the connection with equilibrium properties in the canonical ensemble, Numerical techniques are described in Section 3. Selective chemical applications of the path integral approach are presented in Section 4 and Section 5 concludes. 

If one is interested in equilibrium canonical (fixed temperature) properties of liquid interfaces, an approach to sample phase space is the Monte Carlo (MC) method. Here, only the potential energy function l/(ri,r2,. .., rjy) is required to calculate the probability of accepting random particle displacement moves (and additional moves depending on the ensemble type ). All of the discussion above regarding the boundary conditions, treatment of long-range interactions, and ensembles applies to MC simulations as well. Because the MC method does not require derivatives of the potential energy function, it is simpler to implement and faster to run, so early simulations of liquid interfaces used However, dynamical information is not available with... 

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