Observations of omnipresent suprathermal power law tails, with the unique spectral index of −5, on the velocity distributions of solar wind and pickup ions raise important questions and have far reaching consequences. The obvious question of how these tails are formed during quiet times, when no shocks are present, was previously addressed and is briefly reviewed here. One of the consequences of the existence of ubiquitous quiet time tails is that sufficiently energetic particles are always readily available for further acceleration by shocks. It is this aspect that is examined in this paper. We present observations showing that downstream of two quasi‐stationary shocks the −5 spectral power law spectra are preserved and that the increase in tail pressure jump can be obtained by applying thermodynamic constraints on non‐adiabatic heating of upstream particles by the shock.