B737 ACFT EXITING RWY AFTER LNDG WAS ADVISED BY TWR THAT SMOKE APPEARED TO BE COMING FROM THE R ENG. AFTER SHUTTING DOWN THE ENG GND CTLR ADVISED THE SMOKE WAS FROM THE R TIRE AREA. FLC OBSERVED LOSS OF SYS A HYDS AND HAD GND EMER CREW CHK THE TIRE AREA WHICH BY THEN WAS CLR OF SMOKE OR FIRE. DAMAGED BRAKE ROTOR AND EXTENDED PISTON CAUSED HYD LOSS AND SMOKE.

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FO ACCOMPLISHED A NORMAL FLAPS 30 DEGS VISUAL APCH AND LNDG. WHILE EXITING THE RWY; GND CTL CALLED TO SAY THERE WAS SMOKE COMING FROM THE R ENG. AFTER CONFIRMING THE SMOKE AGAIN; WITH NORMAL COCKPIT INDICATIONS; WE SHUT THE R ENG DOWN. AFTER QUERYING GND AGAIN; THEY SAID THERE WAS STILL SMOKE; BUT IT LOOKED LIKE THE R TIRE. WE TRIED TO CONFIRM THE POSSIBILITY OF HOT BRAKES OR A FLAT TIRE WITH GND CTL AND A NEARBY ACFT ON THE RAMP. WE WERE TOLD THAT THE R TIRE WAS STILL SMOKING AND SOMEONE RADIOED THAT WE MAY WANT TO STOP AS IT LOOKED LIKE THE R TIRE WAS STILL SMOKING. THE CAPT IMMEDIATELY STOPPED THE ACFT AND DIRECTED THE FO TO ASK GND TO ROLL THE EMER EQUIP AS A PRECAUTION AND TO ALLOW THE FIRE CHIEF TO CHK FOR A FIRE HAZARD. THE FO MADE A PA TO THE PAX APPRISING THEM OF THE SIT AND ENSURING NO UNCOMMANDED EVAC. THE FIRE TRUCKS ARRIVED ALMOST IMMEDIATELY. WE HAD LOST SYS A HYDS; SO THE CAPT INITIATED THE APPROPRIATE CHKLIST WHILE THE FO CALLED THE RAMP SUPPORT PEOPLE TO BRING A TUG AND MADE ANOTHER PA TO THE PAX. THE FIRE CHIEF RPTED EVERYTHING AS OK SO WE PINNED THE GEAR AND WERE TOWED THE REMAINING DISTANCE TO THE GATE. MAINT DISCOVERED A BRAKE ROTOR WAS SEVERELY DAMAGED AND THAT LIKELY AN OVEREXTENDED BRAKE PISTON WAS THE SOURCE OF THE HYD LOSS. THE LNDG AND BRAKING WERE NORMAL AND LIKELY THE LEAKING HYD FLUID GOT ON THE HEATED BRAKE AREA AND TIRE CAUSING THE SMOKE RPTED BY GND CTL.