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We seek here to unify the second law of thermodynamics with the other laws,or at least to put up a law behind the second law of thermodynamics. Assumingno fine tuning, concretely by a random Hamiltonian, we argue just fromequations of motion -- but {\em without} second law -- that entropy cannot gofirst up and then down again except with the rather strict restrictionS_{large} \le S_{small 1} + S_{small 2}. Here S_{large} is the "large" entropyin the middle era while S_{small 1} and S_{small 2} are the entropies atcertain times before and after the S_{large} - era respectively. From thistheorem of "no strong maximum for the entropy" a cyclic time S^1 model worldcould have entropy at the most varying by a factor two and would not bephenomenologically realistic. With an open ended time axis (-\infty, \infty)={\bf R} some law behind the second law of thermodynamics is needed if we donot obtain as the most likely happening that the entropy is maximal (i.e. theheat death having already occurred from the start). We express such a lawbehind the second law -- or unification of second law with the other ones -- byassigning a probability weight $P$ for finding the world/the system in variousplaces in phase space. In such a model $P$ is almost unified with the rest as P= exp (-2 ~S_{Im}) with S_{Im} going in as the imaginary part of the action. Wederive quite naturally the second law for practical purposes, a Big Bang withtwo sided time directions and a need for a bottom in the Hamiltonian density.Assuming the cosmological constant is a dynamical variable in the sense that itis counted as "initial condition" we even solve in our model the cosmologicalconstant problem \underline{without} any allusion to anthropic principle.Comment: 12 pages, revtex

Unification of Cosmology and the Second Law of Thermodynamics: -- Proposal for Solving the Cosmological Constant and Inflation Problems --