The problem of determining lower bounds for the energy cost of a given nanoscale design is addressed via a complexity theory-based approach. This paper provides a theoretical framework that is able to assess the trade-offs existing in nanoscale designs between the amount of redundancy needed for a given level of resilience to errors and the associated energy cost. Circuit size, logic depth and error resilience are analyzed and brought together in a theoretical framework that can be seamlessly integrated with automated synthesis tools and can guide the design process of nanoscale systems comprised of failure prone devices. The impact of redundancy addition on the switching energy and its relationship with leakage energy is modeled in detail. Results show that 99% error resilience is possible for fault-tolerant designs, but at the expense of at least 40% more energy if individual gates fail independently with probability of 1%.