A method and arrangement are for heat exchanging in and work exchanging with a working fluid in a heat engine, or a heat pump if the method and its sub-processes are substantially reversed. A thermodynamic cycle for the working fluid is approximately described through the polytropic relation PVn=constant, where P is the pressure, V is the volume and n is the polytropic index of the working fluid with adiabatic index gamma (γ), and wherein the engine consists of at least one working mechanism provided with a first and at least a second volume change chamber, the method comprising in sequence at least the following steps: in a first volume change process, to carry out a first polytropic volume change of the working fluid in a first volume change chamber where n