Shortcuts to isothermality and nonequilibrium work relations.

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Non-equilibrium Systems

Background:

• Conventional thermodynamics mandates quasistatic protocols for isothermal processes.
• Achieving isothermal transitions at finite rates is a significant challenge in non-equilibrium thermodynamics.

Purpose of the Study:

• To propose and design a strategy for finite-rate isothermal transitions, termed "shortcut to isothermality."
• To derive novel nonequilibrium work relations using this strategy.
• To numerically validate these relations in a model system.

Main Methods:

• Development of a theoretical framework for "shortcut to isothermality."
• Derivation of three nonequilibrium work relations: a free-energy difference identity, a Jarzynski-like equality, and a dissipated work-time relationship.
• Numerical simulations of a Brownian particle in a harmonic potential.

Main Results:

• Successful design of a strategy for finite-rate isothermal transitions.
• Derivation of three new nonequilibrium work relations.
• Numerical verification of the derived relations, demonstrating their validity.

Conclusions:

• The proposed "shortcut to isothermality" provides a viable method for rapid isothermal processes.
• The derived nonequilibrium work relations offer new insights into energy dissipation and free-energy changes in driven systems.
• The findings have implications for understanding and controlling non-equilibrium thermodynamic processes.