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I use an UNO R3 with an W5100 Ethernet Shield and i want that the arduino detects when my smartphone is connected to the (wlan) network, is this even possible or do my smartphone have to send an order to arduino if its connected…

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Depending on the smartphone, this can become quite complicated. If your phone is IOS, these basically become invisible when the screen is locked and will not respond to pings. I understand that Android devices are a bit easier to work with for this sort of thing.

Its not an arduino project but you can use a service like IFTTT along with an app on your phone to trigger something when your phone gets to a certain point according to GPS.

https://www.howtogeek.com/221555/how-to-create-geographic-event-triggers-with-your-smartphone-and-ifttt/

Otherwise you could get yourself a wifi device that supports promiscous mode (like an ESP8266) and listen for your phone's MAC address.