Jarzynski Equality is a fundamental relationship in statistical mechanics that connects the work done on a system during a non-equilibrium process to the free energy difference between two states. It highlights the connection between microscopic and macroscopic thermodynamic quantities, showing that the average exponential work over many realizations equals the exponential of the negative free energy difference, expressed mathematically as $$ e^{-\Delta F/k_B T} = \langle e^{-W/k_B T} \rangle $$, where \( \Delta F \) is the free energy difference, \( W \) is the work done, and \( k_B \) is Boltzmann's constant. This equality emphasizes how fluctuations at microscopic scales can influence macroscopic properties, making it especially relevant in quantum thermodynamics.
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