We used the SPIRE/FTS instrument aboard the Herschel Space Observatory (HSO) to obtain the Spectral Line Energy Distributions (SLEDs) of CO from J=4-3 to J=13-12 of Arp 193 and NGC 6240, two classical merger/starbursts selected from our molecular line survey of local Luminous Infrared Galaxies (LIRGs: L_{IR}>=10^{11} L_{sol}). The high-J CO SLEDs are then combined with ground-based low-J CO, {13}CO, HCN, HCO+, CS line data and used to probe the thermal and dynamical states of their large molecular gas reservoirs. We find the two CO SLEDs strongly diverging from J=4-3 onwards, with NGC6240 having a much higher CO line excitation than Arp193, despite their similar low-J CO SLEDs and L_{FIR}/L_{CO,1-0}, L_{HCN}/L_{CO} (J=1-0) ratios (proxies of star formation efficiency and dense gas mass fraction). In Arp193, one of the three most extreme starbursts in the local Universe, the molecular SLEDs indicate a small amount ~(5-15)% of dense gas (n>=10^{4}cm^{-3}) unlike NGC6240 where most of the molecular gas (~(60-70)%) is dense n~(10^4-10^5)cm^{-3}. Strong star-formation feedback can drive this disparity in their dense gas mass fractions, and also induce extreme thermal and dynamical states for the molecular gas.In NGC6240, and to a lesser degree in Arp193, we find large molecular gas masses whose thermal states cannot be maintained by FUV photons from Photon Dominated Regions (PDRs). We argue that this may happen often in metal-rich merger/starbursts, strongly altering the initial conditions of star formation. ALMA can now directly probe these conditions across cosmic epoch, and even probe their deeply dust-enshrouded outcome, the stellar IMF averaged over galactic evolution.
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