  The quantum interest conjecture of Ford and Roman states that any negative
energy flux in a free quantum field must be preceded or followed by a positive
flux of greater magnitude, and the surplus of positive energy grows the further
the positive and negative fluxes are apart. In addition, the maximum possible
separation between the positive and negative energy decreases the larger the
amount of negative energy. We prove that the quantum interest conjecture holds
for arbitrary fluxes of non-interacting scalar fields in 4D Minkowski
spacetime, and discuss the consequences in attempting to violate the second law
of thermodynamics using negative energy. We speculate that quantum interest may
also hold for the Electromagnetic and Dirac fields, and might be applied to
certain curved spacetimes.
