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Recent observations indicate that the eclipsing pulsar binary PSR B1957+20 undergoes alternating epochs of orbital period increase and decrease. We apply a model developed to explain orbital period changes of alternating sign in other close binaries to the PSR B1957+20 system and find that it fits the pulsar observations well. The novel feature of the PSR B1957+20 system is that the energy flow in the companion needed to power the orbital period change mechanism can be supplied by tidal dissipation, making the companion the first identified tidally powered star. The flow of energy in the companion drives magnetic activity, which underlies the orbital period variations. The magnetic activity and the wind driven by the pulsar irradiation results in a torque on the spin of the companion which holds the companion out of synchronous rotation, causing tidal dissipation of energy. We propose that the progenitor system had a $\simeq 2$ hr orbital period and a companion mass of $0.1 - 0.2\>M_\odot$, and the system is evolving to longer orbital periods by mass and angular momentum loss on a time scale of $10^8$ years.
