Qual é o tempo de stand by de uma bateria de 4000 mAh?

Uma bateria de 4000 mAh, com carga completa, durará 4000 horas quando o circuito que alimenta tira 1 mA de corrente.

A mesma bateria com carga completa, durará 4 horas se tirar 1000 mA (1 A).

Tem apenas 1 hora se tirar 4000 mA de corrente.

Se você falar sobre smartphones, eles normalmente desenham 400-500 mA de corrente (avg.) quando estão sendo usados moderadamente. ou seja, usando Facebook, Whatsapp, Instagram, chamadas telefônicas, etc. de vez em quando (digamos 15-20 minutos de cada vez).
Então, em tais situações, a bateria do seu telefone deve durar 8-9 horas.

Se por acaso você jogar pesado ou jogos (Asfalto, Need For Speed etc.), então mais corrente será tirada. Deve ser cerca de 700-800 mA (avg). In that case, the battery will last 5–6 hours.

You get the hang now..

Put the phone in airplane mode, charge the battery and your phone will last a week with 4000 mAh capacity.

Use your phone sightly (internet on, but apps used 4–5 times max), it should last you two days easily.

Explanation:

A battery is a device which stores charge.
The unit of charge is Coulombs. By dimensional analysis (if you studied physics), you will understand that Ampere-Hour simply happens to be an alternative unit for charge.
—————

For non-physics people,
There is a relation which states.

1. Current is the rate of flow of charge. 
2.  
3. I = Q/t  
4.  
5. I=current drawn by the circuit 
6. Q=total charge flowing through the circuit 
7. t=time taken by the charge to complete on run across the circuit 
8.  
9. Unit of current = Ampere 
10. Unit of charge = Coulombs 
11. Unit of time= seconds 
12.  
13. So unit of current, i.e. Ampere is Coulombs per Time (C * t^-1) 
14. i.e. {A = C / s} 
15. subsequently unit of charge becomes, 
16. C = A . s 
17. Charge = current x time 
18. Coulombs is the same as Ampere-second. 
19.  
20. But that is the SI unit, we need something understandable and easier to comprehend. 
21. So, 
22.  
23. we convert it to milliAmpere-hour. 

Hope that answers your question.

Cheers. :)