  We study the phase diagram of spatially inhomogeneous
Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) superconducting state using the
Ginzburg-Landau(GL) free energy, derived from the microscopic Hamiltonian of
the system, and notice that it has a very clear Lifshitz tricritical point. We
find the specific heat jumps abruptly near the first-order line in the emergent
phase diagram which is very similar to the recent experimental observation in
layered organic superconductor. Comparison with experimental data allows us to
obtain quantitative relations between the parameters of phenomenological free
energy. The region of the phase diagram where the specific heat jumps can be
probed by doing a dynamical analysis of the free energy.
