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We measured resistively the critical temperature ${\mathit{T}}_{\mathit{c}}$ and the upper critical field ${\mathit{H}}_{\mathit{c}2}$ of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{4}$${\mathrm{O}}_{8}$ up to a pressure of 18 GPa in magnetic fields up to 10 T, using a cryogenic diamond anvil cell. The onset critical temperature is found to increase from 82 K at ambient pressure to 104 K at 8 GPa at the very large rate of 5.5 K/GPa. At higher pressures, ${\mathit{T}}_{\mathit{c}}$ first saturates and then decreases with increasing pressure. The upper critical field ${\mathit{H}}_{\mathit{c}2}$(T=0 K) is found to strongly decrease up to a pressure of \ensuremath{\sim}8 GPa; at higher pressures, the rate of decrease as a function of pressure is diminished. The large \ensuremath{\partial}${\mathit{T}}_{\mathit{c}}$/\ensuremath{\partial}p at low pressure in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{4}$${\mathrm{O}}_{8}$ can be explained by means of a large change of the number of charge carriers \ensuremath{\delta} in the ${\mathrm{CuO}}_{2}$ planes as a function of pressure. The volume derivative \ensuremath{\partial} ln\ensuremath{\delta}/\ensuremath{\partial} lnV is calculated from our data on ${\mathit{H}}_{\mathit{c}2}$(p) and ${\mathit{T}}_{\mathit{c}}$(p). When the pressure decreases, we find a smaller \ensuremath{\partial}${\mathit{T}}_{\mathit{c}}$/\ensuremath{\partial}p and \ensuremath{\partial}${\mathit{H}}_{\mathit{c}2}$(T=0 K)/\ensuremath{\partial}p due to an irreversible change of the sample above 20 GPa. When the pressure is increased for the second time, we retain the behavior observed at decreasing pressure. The irreversibility in ${\mathit{T}}_{\mathit{c}}$ versus pressure is attributed to an irreversible change in the number of charge carriers.

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