The ballast resistor; An electro-thermal instability in a conducting wire II; Fluctuations around homogeneous stationary states

The correlation function of temperature fluctuations around homogeneous stationary states of the ballast resistor is evaluated by extending the theory of thermal fluctuations around equilibrium states to non-equilibrium situations. It is found that equal-time temperature fluctuations become correlated over large distances if one approaches the critical point. At the “critical point” of the ballast resistor the correlation length and the amplitude of the temperature fluctuations diverge. Furthermore the theory predicts a critical slowing down for the time-dependent temperature fluctuation correlation function. The electric noise of the system is also analyzed.