The connection between thermodynamic entropy and probability

Ergodic Hamiltonian systems with an arbitrary number of degrees of freedom n are considered. A relation is derived connecting the distribution function of the system characteristics with the entropy. It is shown that as n → ∞ it reduces to Einstein's formula /1/. A variational principle for the distribution function, which reduces to the maximum-uncertainty principle as n → ∞ is derived. The principle of maximum entropy for Hamiltonian systems is formulated.