Tractable exploration of phase space

Statistical mechanics is a powerful and elegant theory, at whose core lie the concepts of phase space, probability distributions, and partition functions. With these concepts, statistical mechanics explains physical properties, such as entropy, and physical phenomena, such as irreversibility, all in terms of microscopic properties. 

The invention of digital computers ushered in a new era of computational methods that numerically determine the partition function, rendering feasible the connection between microscopic Hamiltonians and thermodynamic behavior for complex systems. 

Two large classes of computer simulation method were created in the 1940s and 1950s  

Both classes generate ensembles of points in the phase space of a well-defined system. Computer simulations start with a microscopic model of the Hamiltonian. At equilibrium, the determination of the Hamiltonian is sufficient to define the geometry and size of the phase space. With the phase space constraints defined and remembering that macroscopic. 

Without the need to compute the total partition function, we can turn to numerical generation of statistically significant samples of the phase space so as to determine the thermodynamic behavior of matter, beginning with microscopic models. 

---