Around 2008, Entov-Polterovich initiated a program to study the space of functions on symplectic manifolds. By using spectral invariants in Hamiltonian Floer theory, they constructed partial symplectic quasi-states on any closed symplectic manifold. These quasi-states are certain non-linear functionals on the space of functions, which enjoy good symplectic properties and give surprising symplectic rigidity results. In this talk, we will discuss a new functional defined by using relative symplectic cohomology, and compare it with the old definitions. If time permits, applications on dispersion formula and max/min formula will be discussed. Joint with C.Y.Mak and U.Varolgunes.