  A change in a stochastic system has three representations: Probabilistic,
statistical, and informational: (i) is based on random variable
$u(\omega)\to\tilde{u}(\omega)$; this induces (ii) the probability
distributions $F_u(x)\to F_{\tilde{u}}(x)$, $x\in\mathbb{R}^n$; and (iii) a
change in the probability measure $\mathbb{P}\to\tilde{\mathbb{P}}$ under the
same observable $u(\omega)$. In the informational representation a change is
quantified by the Radon-Nikodym derivative $\ln\left( \frac{ d
\tilde{\mathbb{P}}}{ d\mathbb{P}}(\omega)\right)=-\ln\left(\frac{ d F_u}{ d
F_{\tilde{u}}}(x)\right)$ when $x=u(\omega)$. Substituting a random variable
into its own density function creates a fluctuating entropy whose expectation
has been given by Shannon. Informational representation of a deterministic
transformation on $\mathbb{R}^n$ reveals entropic and energetic terms, and the
notions of configurational entropy of Boltzmann and Gibbs, and potential of
mean force of Kirkwood. Mutual information arises for correlated $u(\omega)$
and $\tilde{u}(\omega)$; and a nonequilibrium thermodynamic entropy balance
equation is identified.
