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<γ, and in a second volume change process, to carry out at least one second near-adiabatic or polytropic volume change of the working fluid from a first to a second volume change chamber, where n<γ, or where a volume change starts with n<γ and ands near-adiabatic (n≈γ).

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