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The passivity or positive real condition of passive linear two-terminal-pair networks is introduced. The formulas for thermal noise voltages of these networks are derived by using the Nyquist theorem. A relation between the passivity condition and thermal noise voltages is discussed. From these results, several interesting features of passive one-way systems are derived. For instance, any physically realizable passive one-way system must contain a resistive component dissipating energy. It is not unidirectional with respect to the transmission of heat energy. A method of synthesis for passive linear one-way systems unilateral at all frequencies is treated. Several examples such as electromechanical one-way systems are shown.