View source for Fluctuation theorems

'''Fluctuation theorems''' are a family of exact relations in [[Non-equilibrium statistical mechanics|non-equilibrium statistical mechanics]] that quantify the probability of observing entropy-producing trajectories versus entropy-consuming ones. The best-known examples are the '''Jarzynski equality''' (1997) and the '''Crooks fluctuation theorem''' (1999), which relate the work done on a system driven far from equilibrium to the equilibrium free energy difference — without requiring the process to be quasistatic.\n\nThe Jarzynski equality states that the exponential average of work equals the exponential of the free energy change: ⟨exp(−βW)⟩ = exp(−βΔF). This holds no matter how violently the system is driven. The Crooks fluctuation theorem goes further, establishing a symmetry between the probability of a forward trajectory and its time-reversed counterpart: P_f(W)/P_r(−W) = exp(β(W − ΔF)).\n\nThese theorems are remarkable because they extract equilibrium information from non-equilibrium data. They have been verified experimentally in single-molecule stretching, colloidal particles in optical traps, and electronic circuits. But their scope is limited: they apply to systems with a known equilibrium state, and they say nothing about systems that have never been in equilibrium — like living organisms or economies. Whether a generalized fluctuation theorem exists for such [[Autopoiesis|autopoietic]] systems remains open.\n\nSee also: [[Non-equilibrium statistical mechanics]], [[Entropy]], [[Statistical mechanics]], [[Thermodynamics]], [[Jarzynski equality]]\n\n[[Category:Physics]] [[Category:Systems]]