Skewed thermodynamic geometry and optimal free energy estimation

Area of Science:

• Physics, chemistry, and biology
• Computational science
• Statistical mechanics

Background:

• Free energy differences are crucial in various scientific fields.
• Accurate estimation of free energy is vital for applications like drug discovery.
• Current methods for free energy estimation have limitations in precision and accuracy.

Purpose of the Study:

• To develop design principles for improving free energy estimators.
• To enhance the precision and accuracy of free energy calculations.
• To provide insights applicable to targeted drug discovery screening.

Main Methods:

• Exploiting the connection between work statistics of time-reversed protocol pairs.
• Developing near-equilibrium approximations for moments of excess work.
• Analyzing dominant contributions to precision and accuracy in nonequilibrium estimators.

Main Results:

• Minimum-dissipation protocols follow geodesics of a Riemannian metric within linear response.
• The supra-Stokes tensor introduces a next-order contribution, skewing geometric structure.
• Protocols follow geodesics of a generalized cubic Finsler metric near equilibrium.

Conclusions:

• The supra-Stokes tensor dictates the leading-order bias in bidirectional free energy estimators near equilibrium.
• The developed principles offer a pathway to more accurate free energy calculations.
• These advancements hold potential for accelerating targeted drug discovery.