  A Universe filled with a homogeneous scalar field exhibits `Cosmological
hysteresis'. Cosmological hysteresis is caused by the asymmetry in the equation
of state during expansion and contraction. This asymmetry results in the
formation of a hysteresis loop: $\oint pdV$, whose value can be non-vanishing
during each oscillatory cycle. For flat potentials, a negative value of the
hysteresis loop leads to the increase in amplitude of consecutive cycles and to
a universe with older and larger successive cycles. Such a universe appears to
possess an arrow of time even though entropy production is absent and all of
the equations respect time-reversal symmetry ! Cosmological hysteresis appears
to be widespread and exists for a large class of scalar field potentials and
mechanisms for making the universe bounce. For steep potentials, the value of
the hysteresis loop can be positive as well as negative. The expansion factor
in this case displays quasi-periodic behaviour in which successive cycles can
be both larger as well as smaller than previous ones. This quasi-regular
pattern resembles the phenomenon of BEATS displayed by acoustic systems.
Remarkably, the expression relating the increase/decrease in oscillatory cycles
to the quantum of hysteresis appears to be model independent. The cyclic
scenario is extended to spatially anisotropic models and it is shown that the
anisotropy density decreases during successive cycles if the hysteresis loop is
negative.
