The efficiency of an internal combustion (IC) engine is governed by the thermodynamic cycle underpinning its operation. The thermodynamic efficiency of these devices is primarily determined by the temperature gradient created during the compression process. The final conversion efficiency also known as brake thermal efficiency (BTE) of IC engines, however, also depend on other processes associated with its operation. BTE is a product of the combustion, thermodynamic, gas-exchange, and mechanical efficiencies. The improvement of BTE through maximation of any one of the four efficiencies is reduced by its implication of the other three. Split-cycle engine provides an alternative method of improving the engine efficiency through over-expansion of combustion gases by transferring it to a cylinder of greater volume. The operation of split-cycle engines is based on either the Brayton or the Atkinson Cycles. Atkinson Cycle has been demonstrated in IC engines without the split-cycle architecture but is limited by the reduced energy density. Double Compression Expansion Engine (DCEE) provides a method of accomplishing the Atkinson Cycle without the constraints faced in conventional engine architectures. DCEE splits the compression and expansion processes in a vertical manner that enables the use of larger cylinder volumes for over-expansion as well as first-stage compression without much friction penalties. The present thesis explores the thermodynamic cycle of this novel engine architecture using well-validated 1-dimensional engine models solving for gas-exchange, real gas properties, and heat transfer provided in the GT-Power software tool. The effect of compression ratio, rate of heat addition, sensitivity to design and modeling parameters was assessed and contrasted against conventional engine architecture. The synergies of combining low-temperature combustion (LTC) concepts with DCEE was investigated using simulation and experimental data. DCEE relaxes many constraints placed the operation of an engine in Homogenous Charge Compression Ignition (HCCI) mode. The limitations of adopting Partially Premixed Combustion (PPC) concept is also alleviated by the DCEE concept. BTE improvement of above 10% points is achievable through the DCEE concept along with possibility to achieve very low emissions through use of LTC concepts and new after-treatment methods uniquely available to the DCEE.