Variance-based logic (VBL) uses the fluctuations or the variance in the state of a particle or a physical quantity to represent different logic levels. In this paper, we show that compared to the traditional bi-stable logic representation, the variance-based representation can theoretically achieve a superior performance trade-off (in terms of energy dissipation and information capacity) when operating at fundamental limits imposed by thermal noise. We show that, in addition to the universal KT ln(1/is an element of) energy dissipation required for a single bit fip, a bi-stable logic device needs to dissipate at least 4.35 KT/bit of energy, whereas under similar operating conditions, a VBL device reduces the additional energy dissipation requirements down to sub-KT/bit. These theoretical results are generally enough to be applicable to different instantiations and variants of VBL ranging from digital processors based on energy-scavenging or to processors based on the emerging valleytronic devices.
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