UNAUTHORIZED RWY XING BY ACR.

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RWY CHANGE GIVEN FORM 4L TO 31L ON TAXI AT JFK. TOLD TO HOLD SHORT OF 'J'. PRIOR TO REACHING THAT POINT WAS TOLD TO CROSS 4L TAXI TO 31L. INSTEAD OF TURNING L ON 'J' WE CROSSED 31L WE TAXIED TO 4L. REALIZING ERROR UPON ENTERING 31L WE TAXIED QUICKLY CLR AND STOPPED ON OTHER SIDE. AT NO TIME WAS THERE CONFLICT WITH OTHER TFC. WE SHOULD HAVE BEEN MORE AWARE OF TAXI RTE. SUPPLEMENTAL INFO FROM ACN 198179: REALIZING MY ERROR UPON ENTERING 31L; WE CROSSED AND STOPPED ON OTHER SIDE. AT NO TIME WAS THERE ANY CONFLICT WITH TFC. I SHOULD HAVE BEEN MORE AWARE OF THE TAXI RTE INSTRUCTIONS TO 'TURN L' AT 'J' WOULD HAVE HELPED. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR GAVE TIME IN TYPE. SAYS WX WAS CAVU OR CLOSE TO IT. RWY ASSIGNMENT CHANGE ALSO INVOLVED A CHANGE IN DEP PROC. IT WAS HIS LEG TO FLY SO WAS HEADS DOWN IN COCKPIT REVIEWING NEW SID PROC. SHOULD HAVE BEEN HELPING PIC IN TAXI PROGRESSION. AFTER XING 31L THE TWR GAVE 180 DEG TURN ON TAXIWAY AND CLRNC TO RECROSS 31L TO GET BACK TO TAXIWAY 'J'. DID NOT REVIEW INCIDENT WITH ATC AND HAVE HEARD NO MORE FROM FAA ABOUT IT. RPTR HAD WORKED 7 CONSECUTIVE DAYS AND HAD 24 HRS OFF DUTY PRIOR TO INCIDENT DAY. FELT A BIT 'BURNED OUT'.