Every classical Newtonian mechanical system can be equipped with a
nonstandard Hamiltonian structure, in which the Hamiltonian is the square of
the canonical Hamiltonian up to a constant shift, and the Poisson bracket is
nonlinear. In such a formalism, time translation symmetry can be spontaneously
broken, provided the potential function becomes negative. A nice analogy
between time translation symmetry breaking and the Landau theory of second
order phase transitions is established, together with several example cases
illustrating time translation breaking ground states. In particular, the
ΛCDM model of FRW cosmology is reformulated as the time translation
symmetry breaking ground states.Comment: 10 pages, 1 figure. V2: minor correction