Is there a way to have log4net create log file only when there is logging activity?

Question

We changed our log4net file name to include the current date but only want log files created on those dates that there is logged activity. This is our current configuration:

<log4net>
    <appender name="RollingFileAppender" type="log4net.Appender.RollingFileAppender">
        <file type="log4net.Util.PatternString" value="{0}\\logfiles\\log%date{{yyyyMMdd}}-${{COMPUTERNAME}}.log" />
        <appendToFile value="true" />
        <lockingModel type="log4net.Appender.FileAppender+MinimalLock" /> 
        <rollingStyle value="Size" />
        <maxSizeRollBackups value="10" />
        <maximumFileSize value="10MB" />
        <staticLogFileName value="true" />
        <layout type="log4net.Layout.PatternLayout">
            <conversionPattern value="%date %-5level %logger %message%newline" />
        </layout>
    </appender>
    <root>
        <level value="WARN" />
        <appender-ref ref="RollingFileAppender" />
    </root>
</log4net>

It's producing empty files on days when the logger is created but no messages of WARN or greater are written. Is there a configuration to prevent empty files?