Fluctuation theorems 1-4 describe nonequilibrium stochastic behaviour in small systems. Whilst experiments have shown that fluctuation theorems are obeyed by single particles in liquids 5 and several other physical systems 6-10 , it has not been shown if that is the case in strongly coupled plasmas. Plasmas are said to be strongly coupled when interparticle potential energies are large compared to kinetic energies. Charged particles in such plasmas can behave collectively like liquids 11,12 , but with essential di erences, such as long-range collisions 13 . It remains unexplored whether, despite these di erences, the stochastic behaviour of strongly coupled plasmas will obey fluctuation theorems. Here we demonstrate experimentally that a strongly coupled dusty plasma obeys the fluctuation theorem of Evans, Cohen, and Morriss (ECM) 14 , which was developed for a simple liquid in a nonequilibrium steady state. This fluctuation theorem describes the entropy production arising from collisions in a steady laminar shear flow.A dusty plasma 15-17 is a four-component mixture of microspheres, electrons, positive ions, and a rarefied neutral gas, which all share a volume 18 . The microspheres, which are the heaviest of these components, develop large charges 19 so that they become strongly coupled 20 . The lighter charged components of the dusty plasma (electrons and positive ions) are weakly coupled. Dusty plasmas have much in common with other strongly coupled plasmas, such as ultracold neutral plasmas 21 , and warm dense matter 22 as well.The collection of microspheres can undergo a liquid-like flow when external forces are applied by laser beams [23][24][25][26][27] . In this way, the microspheres can be driven into a shear flow-that is, a flow with a transverse gradient in the flow velocity. In the shear flow, entropy production results from collisions between microspheres.Many fluctuation theorems centre on the rate of entropy production in nonequilibrium systems below the thermodynamic limit. Fluctuation theorems (not to be confused with the similarly named fluctuation-dissipation theorem) all spawned from the ECM fluctuation theorem; this original fluctuation theorem was developed especially for a steady-state laminar shear flow. In a shear flow, entropy production is generated by viscous heating. This viscous heating is always positive in the thermodynamic limit, but it can fluctuate briefly to negative values for a subsystem within the fluid, containing a small number of molecules. These fluctuations, with negative heating and therefore negative entropy production, have been described as violations of the second law of thermodynamics 14 .The ECM fluctuation theorem compares these negative-entropyproduction fluctuations to the more common positive fluctuations. In particular, the probabilities of these two kinds of fluctuations are predicted to have a ratio obeying 14,28 ln p(We will later summarize equation (1), which is the historically important ECM fluctuation theorem, as left-hand side equals righthand side ...