For several decades, researchers studying the physics of computation have known that physics, as it is currently understood, sets no fundamental lower bound on the energy expenditure required for computation, in the case where the computation is performed reversibly, i.e., without discarding information.
If, on the other hand, a bit of information is thrown away (meaning
that a computational state is reached that could have been reached
from either of two preceding states), then the second law of
thermodynamics requires an unavoidable energy dissipation of 
, where 
is Boltzmann's constant and T is the temperature of
the system. Current digital circuit technologies actually dissipate
around six orders of magnitude more energy than this minimum whenever
a bit is erased, because bit erasure is done by dumping large numbers
of electrons from a high-voltage circuit node down to ground. But
even this much larger energy dissipation can be avoided if the
computation is done reversibly, using adiabatic circuit techniques
such as SCRL [7].
The energy dissipated when bits are erased becomes a serious problem as we extrapolate current trends in computer technology to ever-higher component densities and speeds. If every logic element erases a bit (namely, its previous output) on every cycle, as typically occurs in current digital circuits, the rate of heat production will eventually exceed the heat flow capacity of the computing material, leading to high temperatures and thermal noise that can prevent circuits from functioning properly. Active cooling, e.g., with coolant flowing through channels in the computing material, will eventually be required, leading to severe logistical problems of its own. Moreover, in mobile computing devices, the total power and/or energy available for computation is usually limited, and will thus restrict the total rate and/or amount of computation that the device can perform.
Reversibility offers a way to deal with these problems. If we can avoid discarding most or all of the information that current computers throw away, we can reduce the energy that is dissipated to heat, allowing faster computation with a given rate of cooling, or more computation for a given supply of energy.
Full reversibility also offers potential benefits unrelated to energy usage, namely, for detecting errors, preventing tampering, and diagnosis of software problems. I will discuss these other benefits in more detail in the thesis, but not in this short proposal.