  Fluctuations arising in nonlinear dissipative systems (diode, transistors,
chemical reaction, etc.) subject to an external drive (voltage, chemical
potential, etc.) are well known to elude any simple characterization such as
the fluctuation-dissipation theorem (also called Johnson-Nyquist law, or
Einstein's law in specific contexts). Using results from stochastic
thermodynamics, we show that the variance of these fluctuations exceeds the
variance predicted by a suitably extended version of Johnson-Nyquist's formula,
by an amount that is controlled by the skewness (third moment) of the
fluctuations. As a consequence, symmetric fluctuations necessarily obey the
extended Johnson-Nyquist formula. This shows the physical inconsistency of
Gaussian approximation for the noise arising in some nonlinear models, such as
MOS transistors or chemical reactions. More generally, this suggests the need
for a stochastic nonlinear systems theory that is compatible with the teachings
of thermodynamics.
