Thermodynamics of one-dimensional nonlinear lattices

Analytic equations were obtained for the thermodynamic parameters of one-dimensional lattices of particles with the Toda and Morse interaction potentials in a canonical Gibbs ensemble. For the same systems, equations were derived for molecular dynamics simulations of thermodynamic processes. Stochastic differential equations were solved with simulating the thermostat by Langevin sources with random forced. Analytic equations for thermodynamic parameters (energy, temperature, and pressure) excellently coincided with molecular dynamics simulation results. The kinetics of system relaxation to the thermodynamic equilibrium state was analyzed. The advantages of simulating the physical properties of systems in a canonical compared with microcanonical ensemble were demonstrated.