A split-cycle engine, comprising: a compression cylinder, comprising: an inlet port for a first working fluid; a coolant admission port; an outlet port for the first working fluid and coolant; and a compression piston, having an obverse face and a reverse face, the compression piston being arranged within the compression cylinder such that the compression piston separates a first volume of the compression cylinder, the first volume for containing the first working fluid, from a second volume of the compression cylinder, the second volume for containing a second working fluid, the first volume being defined by the obverse face and an inner wall of the compression cylinder and including the ports, and the second volume being defined by the reverse face and the inner wall of the compression cylinder; an expansion cylinder, comprising: an inlet port for the first working fluid, the inlet port being arranged in fluidic communication with the compressor outlet port; a fuel admission port; an exhaust port for the exit of an exhaust product of combustion; and an expansion piston, having an obverse face and a reverse face, the expansion piston being arranged within the expansion cylinder such that the expansion piston separates a first volume of the expansion cylinder, the first volume for containing the first working fluid, from a second volume of the expansion cylinder, the second volume for containing second working fluid, the first volume being defined by the obverse face and an inner wall of the expansion cylinder and including the ports, and the second volume being defined by the reverse face and the inner wall of the expansion cylinder; and a fluid coupling between the second volume of the compression cylinder and the second volume of the expansion cylinder, wherein the two second volumes and the fluid coupling provide a closed volume for the second working fluid, wherein the fluid coupling comprises a regenerator arranged such that the two second volumes are thermally decoupled. a compression cylinder, comprising: an inlet port for a first working fluid; a coolant admission port; an outlet port for the first working fluid and coolant; and a compression piston, having an obverse face and a reverse face, the compression piston being arranged within the compression cylinder such that the compression piston separates a first volume of the compression cylinder, the first volume for containing the first working fluid, from a second volume of the compression cylinder, the second volume for containing a second working fluid, the first volume being defined by the obverse face and an inner wall of the compression cylinder and including the ports, and the second volume being defined by the reverse face and the inner wall of the compression cylinder; an inlet port for a first working fluid; a coolant admission port; an outlet port for the first working fluid and coolant; and a compression piston, having an obverse face and a reverse face, the compression piston being arranged within the compression cylinder such that the compression piston separates a first volume of the compression cylinder, the first volume for containing the first working fluid, from a second volume of the compression cylinder, the second volume for containing a second working fluid, the first volume being defined by the obverse face and an inner wall of the compression cylinder and including the ports, and the second volume being defined by the reverse face and the inner wall of the compression cylinder; an expansion cylinder, comprising: an inlet port for the first working fluid, the inlet port being arranged in fluidic communication with the compressor outlet port; a fuel admission port; an exhaust port for the exit of an exhaust product of combustion; and an expansion piston, having an obverse face and a reverse face, the expansion piston being arranged within the expansion cylinder such that the expansion piston separates a first volume of the expansion cylinder, the first volume for containing the first working fluid, from a second volume of the expansion cylinder, the second volume for containing second working fluid, the first volume being defined by the obverse face and an inner wall of the expansion cylinder and including the ports, and the second volume being defined by the reverse face and the inner wall of the expansion cylinder; and an inlet port for the first working fluid, the inlet port being arranged in fluidic communication with the compressor outlet port; a fuel admission port; an exhaust port for the exit of an exhaust product of combustion; and an expansion piston, having an obverse face and a reverse face, the expansion piston being arranged within the expansion cylinder such that the expansion piston separates a first volume of the expansion cylinder, the first volume for containing the first working fluid, from a second volume of the expansion cylinder, the second volume for containing second working fluid, the first volume being defined by the obverse face and an inner wall of the expansion cylinder and including the ports, and the second volume being defined by the reverse face and the inner wall of the expansion cylinder; and a fluid coupling between the second volume of the compression cylinder and the second volume of the expansion cylinder, wherein the two second volumes and the fluid coupling provide a closed volume for the second working fluid, wherein the fluid coupling comprises a regenerator arranged such that the two second volumes are thermally decoupled.