Jarzynski Two-State Quench

The Jarzynski equality connects the non-equilibrium work fluctuations of a process to the equilibrium free-energy difference between the initial and final states. This module explores a simple two-state system undergoing an instantaneous energy quench.

Experiment

You can interactively explore the relationship between the exponential work average and the free-energy difference in the Jarzynski Two-State Quench module.

1. Change the Inverse temperature to observe how it affects the initial state probabilities and the resulting exponential weighting.
2. Adjust the Initial excited energy and Final excited energy to simulate different instantaneous quench scenarios.
3. Observe that while the Mean work is generally greater than or equal to the Free-energy difference (in accordance with the Second Law of Thermodynamics and Jensen's inequality), the Exponential work average perfectly matches the Partition-function ratio.
4. Notice that negative work and free-energy changes are possible for downward quenches (where the final energy is lower than the initial energy), but the mean dissipated work remains non-negative.