A B757 FLT CREW IS NOTIFIED BY COMPANY THAT THEY LEFT THE ACFT WITH AN ENG RUNNING.

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IT WAS BROUGHT TO MY ATTN THAT THE L ENG WAS RUNNING UNATTENDED AT GATE ON ARR AT THE HOTEL FOR SCHEDULED LAYOVER. TO THE BEST OF MY KNOWLEDGE AND RECALL; BOTH ENGS WERE SHUT DOWN IN NORMAL SEQUENCE USING STANDARD COMPANY PROCS; SOP AND THE ACFT WAS SECURED FOR A NORMAL EXTENDED OVERNIGHT. THE R ENG WAS SHUT DOWN APCHING THE GATE AND L ENG WAS SHUT DOWN 4-5 MINS AFTER THE PARKING BRAKE WAS SET AND AFTER GND PWR WAS PLUGGED IN AND ACCEPTED. I SELECTED GND PWR TO 'ON' AND COMMANDED THE FO TO SHUT DOWN THE L ENG. I CONFIRMED THE START SWITCH WAS PLACED IN THE CUTOFF POS AND VERIFIED THAT THE L ENG FUEL FLOW WAS ZERO PRIOR TO DIMMING THE ENG CRT'S. MOST COCKPIT LIGHTS AND FLT INST CRT'S HAD BEEN TURNED OFF OR DIMMED PRIOR TO THE L ENG BEING SHUT DOWN. THE REMAINING LIGHTS; BATTERY SWITCH AND STANDBY PWR SWITCH WERE TURNED OFF AND THE 'YELLOW' CIRCUIT BREAKERS WERE PULLED PRIOR TO EXITING THE COCKPIT. AFTER GATHERING MY BAGS; I WENT TO THE CABIN; WHERE ALL FIRST CLASS PAX HAD DEPLANED AND PROCEEDED TO DOOR 2L TO 'SAY MY GOODBYES' TO THE REMAINING COACH PAX AND JOKED WITH A FLT ATTENDANT ABOUT THE OUTCOME OF THE FOOTBALL GAME. WITH THE L ENG RUNNING; I AM SURE THE NOISE WOULD HAVE GOTTEN MY ATTN. I NORMALLY WOULD FIND MYSELF AT 2L AT CONCLUSION OF MOST FLTS ON THE B757 AND DID NOT SENSE ANYTHING OUT-OF-ORDINARY. MY CONVERSATION WITH PAX AND FLT ATTENDANTS WAS NORMAL -- NOT STRAINED. I LEFT THE ACFT WITH 1 PAX WAITING FOR A WHEELCHAIR TO ARRIVE. WE WERE NOT HURRIED OR RUSHED DURING THIS TIME PERIOD. IF THE L ENG WAS LEFT RUNNING; I CAN ONLY SPECULATE AS TO HOW IT HAPPENED. FLT CREW COM AND CRM WAS GOOD. COMPANY PROCS AND SOPS WERE FOLLOWED. THIS TRIP WAS A 4 DAY TRIP FOLLOWING A 3 DAY TRIP WITH 1 DAY OFF BTWN THE TRIP FOR PERSONAL BUSINESS. IF FATIGUE WAS A FACTOR; I CAN NOT IDENT IT; BUT IT'S ALWAYS A POSSIBILITY AT THE END OF THE WORK DAY.