We explore the relation between the star formation rate surface density ($Sigma$SFR) and the interstellar gas pressure for nearby compact starburst galaxies. The sample consists of 17 green peas and 19 Lyman break analogs. Green peas are nearby analogs of Ly$alpha$ emitters at high redshift and Lyman break analogs are nearby analogs of Lyman break galaxies at high redshift. We measure the sizes for green peas using Hubble Space Telescope Cosmic Origins Spectrograph (COS) NUV images with a spatial resolution of $sim$ 0.05$^{}$. We estimate the gas thermal pressure in HII regions by $P = N_{total}Tk{_B} simeq 2n_{e}Tk{_B}$. The electron density is derived using the [SII] doublet at 6716,6731 AA, and the temperature is calculated from the [OIII] lines. The correlation is characterized by $Sigma$ SFR = 2.40$times$10$^{-3,}$M$_{odot,}$yr$^{-1,}$kpc$^{-2}$$left(frac{P/k_{B}}{10^{4}cm^{-3}K}right)^{1.33}$. Green peas and Lyman break analogs have high $Sigma$SFR up to 1.2 M$_{odot,}$yr$^{-1,}$kpc$^{-2}$ and high thermal pressure in HII region up to P/k$_B$ $sim$10$^{7.2}{rm, K, cm}^{-3}$. These values are at the highest end of the range seen in nearby starburst galaxies. The high gas pressure and the correlation, are in agreement with those found in star-forming galaxies at z $sim$ 2.5. These extreme pressures are shown to be responsible for driving galactic winds in nearby starbursts. These outflows may be a crucial in enabling Lyman-$alpha$ and Lyman-continuum to escape.
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