  Finite heat reservoir capacity and temperature fluctuations lead to
modification of the well known canonical exponential weight factor. Requiring
that the corrections least depend on the one-particle energy, we derive a
deformed entropy, K(S). The resulting formula contains the Boltzmann-Gibbs, the
Renyi and the Tsallis formulas as particular cases. For extreme large
fluctuations (compared to the Gaussian case) a new, parameter-free entropy -
probability relation emerges. This formula and the corresponding canonical
equilibrium distribution are nearly Boltzmannian for high probability, but
deviate from the classical result for low probability. In the extreme large
fluctuation limit the canonical distribution resembles for low probability the
cumulative Gompertz distribution.
