Temperatures: old, new and middle aged

This study explores the various ways in which a ‘temperature’ can be introduced and calculated in a molecular simulation. We focus on the relatively recent formula of Rugh, and a simplified version called the ‘configurational’ temperature, T config, which became popular after Rugh's work. We derive formulae for these various ‘temperatures’ for the special case of the soft–sphere fluid, with the pair interaction, , where e and σ set the energy and length scales, respectively, and for different n values. We show with a number of simple test cases that the various prescriptions of temperature give the same result as the thermodynamic temperature at equilibrium. Although much of the current work uses the configurational temperature, Rugh's temperature, T R, has the advantage that it has the thermodynamic value in circumstances where the configurational temperature is not defined (such as in the limit of the ideal gas, where Rugh's temperature becomes the kinetic temperature). The configurational temperature i...