There are no "travel days" in the playoffs, so players do not get rest between games where park changes occur. In the playoffs and TOC, teams will get rest if they clinch their series in fewer games than their next opponent clinched theirs. For example, a team that sweeps the LCS 4-0 will be credited three days of rest if their World Series opponent won the LCS in a seven game series 4-3.
There are no random energy bumps at any time. All rest is programmed for specific instances only.