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For example, process notepad.exe created there should be a log entry in the log file.

Is there any such tool in windows?

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Process Lasso fits your needs, plus more powerful features

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Mark Russinovich created the tool Sysmon which logs activity in Windows:

System Monitor (Sysmon) is a Windows system service and device driver that, once installed on a system, remains resident across system reboots to monitor and log system activity to the Windows event log. It provides detailed information about process creations, network connections, and changes to file creation time.

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Look if this tool is enough and logs the information you need.

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