Fundamental energy cost of finite-time parallelizable computing

The fundamental energy cost of irreversible computing is given by the Landauer bound of kT ln 2/bit, where k is the Boltzmann constant and T is the temperature in Kelvin. However, this limit is only achievable for infinite-time processes. We here determine the fundamental energy cost of finite-time parallelizable computing within the framework of nonequilibrium thermodynamics. We apply these results to quantify the energetic advantage of parallel computing over serial computing. We find that the energy cost per operation of a parallel computer can be kept close to the Landauer limit even for large problem sizes, whereas that of a serial computer fundamentally diverges. We analyze, in particular, the effects of different degrees of parallelization and amounts of overhead, as well as the influence of non-ideal electronic hardware. We further discuss their implications in the context of current technology. Our findings provide a physical basis for the design of energy-efficient computers.

Automated summary

In this study, we determine the fundamental energy cost of finite-time parallelizable computing and quantify the energetic advantage of parallel computing over serial computing. It is found that the energy cost per operation of a parallel computer can approach the Landauer limit even for large problem sizes, while that of a serial computer diverges fundamentally. The effects of different degrees of parallelization, overhead amounts, and non-ideal electronic hardware are analyzed, along with their implications in the context of current technology.