Free-energy estimates from nonequilibrium trajectories under varying-temperature protocols

Area of Science:

• Statistical mechanics
• Non-equilibrium thermodynamics
• Physical chemistry

Background:

• The Jarzynski equality enables free-energy difference calculations from nonequilibrium work measurements.
• High work fluctuations necessitate numerous trajectories, limiting practical application.
• Standard Jarzynski equality is inapplicable to protocols involving temperature variations.

Purpose of the Study:

• To derive a generalized Jarzynski equality applicable to varying-temperature protocols.
• To investigate the convergence properties of the modified equality compared to the standard version.
• To extend the framework of non-equilibrium statistical mechanics to more complex experimental designs.

Main Methods:

• Derivation of a modified Jarzynski equality within Markovian stochastic dynamics.
• Development of an associated fluctuation relation for varying-temperature processes.
• Analysis of convergence properties through theoretical comparison.

Main Results:

• A novel variant of the Jarzynski equality valid for protocols with changing temperatures was derived.
• The modified equality demonstrates superior convergence properties compared to the standard Jarzynski equality.
• The derivation is consistent with existing methods in Hamiltonian dynamics.

Conclusions:

• The developed modified Jarzynski equality expands the applicability of non-equilibrium free-energy calculations.
• Varying-temperature protocols can be efficiently analyzed, potentially reducing computational cost.
• This work provides a valuable tool for studying complex systems in statistical and physical chemistry.