Hybrid thermodynamic compressor for compressing a working fluid, the compressor comprising at least: - one volumetric cylinder and one thermal cylinder connected to each other mechanically by a connecting rod system and pneumatically by a connection circuit, - one reversible electric machine connected to the connecting rod system, the volumetric cylinder comprising a cylindrical enclosure with a first piston which separates a first chamber from a second chamber, the thermal cylinder comprising a cylindrical enclosure with a second piston which separates a third chamber, called cold chamber, from a fourth chamber, which can be brought into thermal contact with a heat source to become a hot chamber, and thus generate a cycled movement in the thermal cylinder, the connection circuit connecting the second chamber with the third chamber, and concerning the connecting rod system, the first piston is connected to a rotor by a first connecting rod assembly, and the second piston is connected, directly or indirectly, to said rotor by a second connecting rod assembly, with a predetermined angular offset (θd) provided by the connecting rod system between the cycle of the first piston and the cycle of the second piston, the volumetric cylinder being equipped with an inlet path with a first non-return valve and an outlet path with a second non-return valve, to deliver the working fluid at a second pressure (Pout), and wherein the power produced in the thermal cylinder is transmitted to the volumetric cylinder essentially via the connection circuit and not via the connecting rod system. - one volumetric cylinder and one thermal cylinder connected to each other mechanically by a connecting rod system and pneumatically by a connection circuit, - one reversible electric machine connected to the connecting rod system, the volumetric cylinder comprising a cylindrical enclosure with a first piston which separates a first chamber from a second chamber, the thermal cylinder comprising a cylindrical enclosure with a second piston which separates a third chamber, called cold chamber, from a fourth chamber, which can be brought into thermal contact with a heat source to become a hot chamber, and thus generate a cycled movement in the thermal cylinder, the connection circuit connecting the second chamber with the third chamber, and concerning the connecting rod system, the first piston is connected to a rotor by a first connecting rod assembly, and the second piston is connected, directly or indirectly, to said rotor by a second connecting rod assembly, with a predetermined angular offset (θd) provided by the connecting rod system between the cycle of the first piston and the cycle of the second piston, the volumetric cylinder being equipped with an inlet path with a first non-return valve and an outlet path with a second non-return valve, to deliver the working fluid at a second pressure (Pout), and wherein the power produced in the thermal cylinder is transmitted to the volumetric cylinder essentially via the connection circuit and not via the connecting rod system. the thermal cylinder comprising a cylindrical enclosure with a second piston which separates a third chamber, called cold chamber, from a fourth chamber, which can be brought into thermal contact with a heat source to become a hot chamber, and thus generate a cycled movement in the thermal cylinder, the connection circuit connecting the second chamber with the third chamber, and concerning the connecting rod system, the first piston is connected to a rotor by a first connecting rod assembly, and the second piston is connected, directly or indirectly, to said rotor by a second connecting rod assembly, with a predetermined angular offset (θd) provided by the connecting rod system between the cycle of the first piston and the cycle of the second piston, the volumetric cylinder being equipped with an inlet path with a first non-return valve and an outlet path with a second non-return valve, to deliver the working fluid at a second pressure (Pout), and wherein the power produced in the thermal cylinder is transmitted to the volumetric cylinder essentially via the connection circuit and not via the connecting rod system.