  As the size of transistors approaches the mesoscopic scale, existing energy
consumption analysis methods exhibit various limits, especially when being
applied to describe the non-equilibrium information processing of transistors
at ultra-low voltages. The stochastic thermodynamics offers a theoretic tool to
analyze the energy consumption of transistor during the non-equilibrium
information processing. Based on this theory, an information energy ratio of
XOR gate composed of single-electron transistors is proposed at the mesoscopic
scale, which can be used to quantify the exchange between the information and
energy at XOR gates. Furthermore, the energy efficiency of the parity check
circuit is proposed to analyze the energy consumption of digital signal
processing systems. Compared with the energy efficiency of parity check circuit
adopting the 7 nm semiconductor process supply voltage, simulation results show
that the energy efficiency of the parity check circuit is improved by 266% when
the supply voltage is chosen at a specified value.
