Temperature Integration: an efficient procedure for calculation of free energy differences

TL;DR

Temperature Integration is a new efficient method for calculating free energy differences between systems with similar degrees of freedom, especially useful for rough energy landscapes, by leveraging parallel tempering and lnZ differences at two temperatures.

Contribution

The paper introduces Temperature Integration, a novel approach that simplifies free energy calculations using temperature differences and parallel tempering, applicable to systems with known phase space volume.

Findings

Demonstrated efficiency on a toy model of hard rods on a 1D ring

Allows calculation of absolute free energy if phase space volume is known

Applicable to systems with rough energy landscapes

Abstract

We propose a method, Temperature Integration, which allows an efficient calculation of free energy differences between two systems of interest, with the same degrees of freedom, which may have rough energy landscapes. The method is based on calculating, for each single system, the difference between the values of lnZ at two temperatures, using a Parallel Tempering procedure. If our two systems of interest have the same phase space volume, they have the same values of lnZ at high-T, and we can obtain the free energy difference between them, using the two single-system calculations described above. If the phase space volume of a system is known, our method can be used to calculate its absolute (versus relative) free energy as well. We apply our method and demonstrate its efficiency on a toy model of hard rods on a 1-dimensional ring.