  This early work met with vigorous objections. H. Poincaré had proven a recurrence theorem for bounded dynamical systems that seemed to contradict the monotonic approach to equilibrium demanded by thermodynamics. Poincaré's theorem showed that any appropriately bounded system in which energy was conserved would of necessity, over an infinite time, return an infinite number of times to states arbitrarily close to the initial dynamical state in which the system was started. J. Loschmidt argued that the time irreversibility of thermodynamics was incompatible with the symmetry under time reversal of the classical dynamics assumed to govern the motion of the molecular constituents of the object.