In the Eidos forums user chip5541 published the alleged system requirements of Batman: Arkham Asylum. Currently there is no information if those are the correct requirements though.
Minimal System Requirements
• CPU: Intel single-core with 3 GHZ
• RAM: Windows XP = 1 GiByte, Windows Vista = 2 GiByte
• Graphics card: Nvidia Geforce 6600 or Ati Radeon 1300
Recommended System Requirements
• CPU: Intel Pentium D 3 GHz or AMD Athlon 64 X2 3800+ (dual-core)
• RAM: Windows XP = 2 GiByte, Windows Vista = 3 Gibyte
• Graphics card: Nvidia Geforce 7900 GT
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Batman: Arkham Asylum said to be coming in Q3 2009, but an exact release date has not been announced yet.