Fluctuations of the Phase Difference across an Array of Josephson Junctions in Superfluid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">H</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mn>4</mml:mn></mml:mmultiscripts></mml:math>near the Lambda Transition

We present a formal thermodynamic treatment of superfluid flow in a Josephson junction. We show that the current i(s) and the phase difference phi are thermodynamic conjugate variables. We derive quantitative expressions for the rms fluctuations of i(s) and phi. Also, we discuss the thermodynamic stability and the thermal activation to the phase-slip region. We apply the developed formalism to show why an array of apertures in 4He can exhibit the Josephson effect near the lambda transition despite strong thermal fluctuations.