Computer Simulations

Abstract

Computer simulations have become an important tool in statistical mechanics, since they allow the study of systems in conditions hardly accessible to experimental observations. Furthermore, they are useful to assert, at least in some situations, the very foundations of macroscopic formalisms. In particular, in equilibrium, computer simulations have been especially fruitful in the analysis of the equations of state and phase transitions of systems composed of interacting particles; out of equilibrium, they are very helpful in the calculation of transport coefficients and in the formulation of non-equilibrium thermodynamics beyond the local-equilibrium approximation. However, out of local equilibrium several conceptual problems arise which are not present in equilibrium, as, for instance, the definition of temperature or pressure and their relation with measurements.

The interpretation of the results provided by computer simulations relies on assumptions such as the meaning of temperature (which is usually identified as the kinetic temperature) and the kind of average to be performed to obtain truly significant macroscopic results. As a consequence, a detailed comparison of the results of simulations with experimental observations may shed a critical view on these crucial and subtle matters. Most attention has been focused on the calculation of transport coefficients out of equilibrium in the linear regime, and more recently the non-linear regime has been the subject of active research. In particular, non-equilibrium equations of state and non-linear transport equations have been extensively studied by Evans and collaborators (Evans and Morriss 1990); in this chapter we will pay special attention to their contributions and emphasize the aspects which are most closely related to extended irreversible thermodynamics.