Towards bulk thermodynamics via non-equilibrium methods: gaseous methane as a case study

We illustrate how the Jarzynski equality (JE), which is the progenitor of non-equilibrium methods aimed at constructing free energy landscapes for molecular-sized fluctuating systems subjected to steered transformations, can be applied to derive equations of state for bulk systems. The key-step consists of physically framing the computational strategy of “total energy morphing”, recently presented by us as an efficient implementation of the JE [M. Zerbetto, A. Piserchia, D. Frezzato, J. Comput. Chem., 2014, 35, 1865–1881], in terms of build-up of the real thermodynamic state of a bulk material from the corresponding ideal state, in which the particles are non-interacting. In this context, the JE machinery yields the excess free energy versus suitably chosen controlled state variables, whose thermodynamic derivatives eventually lead to the equation of state. As an explanatory case study, we apply the methodology to derive the equation of state of gaseous methane by constructing the Helmholtz free energy versus the particle density (at fixed temperature) and then evaluating the thermodynamic derivative with respect to the volume. In our intent, this “old-style” work on gaseous methane should open the way for the investigation of thermodynamics of extended systems via non-equilibrium methods.