Taishi Namba

Sharp criterion for the coarse-grained arrow of time in Hamiltonian dynamics

The Gibbs entropy of a Hamiltonian ensemble is constant, and the growth of entropy is commonly attributed to coarse-graining. We ask when Gaussian coarse-graining actually guarantees that the coarse-grained entropy does not decrease, for every initial ensemble. For linear Hamiltonian flows we prove a necessary and suff...