Compare-Object & get-wmiobject win32_process does it right

Hello
the fasted way to have lots of processes with the same ProcessName is use Chrome, which opens for each tab its own process and uses a few of it's own. I heard rumours that firefox will use seperate processes in future versions too. But here I'm not going to start any process vs. thread discussion. Here I will play with processes with the same name. You can just start Notepad for this purpose.

get-process | ? {$_.Name -eq 'Notepad' } | Kill            
            
            
Notepad            
Notepad            
notepad            
notepad            
            
$gp_a = get-process notepad             
$gwmip_a = get-wmiobject win32_process | ? {$_.Name -eq 'notepad.exe'}            

The code above just ensures, that there are 4 instances of notepad running.
Next close one of the first 3 instances and take fresh snapshots.

$gp_b = get-process notepad             
$gwmip_b = get-wmiobject win32_process | ? {$_.Name -eq 'notepad.exe'}            

Let's look at them:

$gp_a            

Initially there where 4 processes:

PS C:\Var\bin> $gp_a

Handles  NPM(K)    PM(K)      WS(K) VM(M)   CPU(s)     Id ProcessName                                                        
-------  ------    -----      ----- -----   ------     -- -----------                                                        
     69       3      992       7612    72            1492 notepad                                                            
     69       3      976       4220    55            2272 notepad                                                            
     68       3      972       4096    55            3368 notepad                                                            
     13       1      284         60     2            5480 notepad                                                            

$gp_b

In second snapshot there are 3 processes (PID 2272 got killed)

PS C:\Var\bin> $gp_b

Handles  NPM(K)    PM(K)      WS(K) VM(M)   CPU(s)     Id ProcessName                                                        
-------  ------    -----      ----- -----   ------     -- -----------                                                        
     72       3     1012       7852    59            1492 notepad                                                            
     72       3     1012       7800    59            3368 notepad                                                            
     72       3     1020       7960    59            5480 notepad                                                            

Compare-Object $gp_a $gp_b |             
    Where-object {$_.SideIndicator -ne '=='} |             
    Select  -ExpandProperty InputObject            

Trying to use Compare-Object on the results of get-Process, as recommended in http://technet.microsoft.com/en-us/library/ee156812.aspx I get a wrong result

PS C:\Var\bin> Compare-Object $gp_a $gp_b | 
    Where-object {$_.SideIndicator -ne '=='} | 
    Select  -ExpandProperty InputObject


Handles  NPM(K)    PM(K)      WS(K) VM(M)   CPU(s)     Id ProcessName                                                        
-------  ------    -----      ----- -----   ------     -- -----------                                                        
     13       1      284         60     2            5480 notepad                                                            

(Compare-Object $gwmip_a $gwmip_b |             
    Where-object {$_.SideIndicator -ne '=='}).Inputobject |            
    Select ProcessId, Name            

while good old WMI gives the correct answer

PS C:\Var\bin> (Compare-Object $gwmip_a $gwmip_b | 
    Where-object {$_.SideIndicator -ne '=='}).Inputobject |
    Select ProcessId, Name


                                                     ProcessId Name                                                          
                                                     --------- ----                                                          
                                                          2272 notepad.exe                                                   

The documentation of Compare-Object contains the funny sentense:

The result of the comparison indicates whether a property value appeared only in the object from the Reference set (indic
ated by the <= symbol), only in the object from the Difference set (indicated by the => symbol) or, if the IncludeEqual p
arameter is specified, in both objects (indicated by the == symbol).

Does it chose a property by incident and in the case of Get-Process, does it use ProcessName instead of Id ?


Is there someone who can tell more about the logic Compare-Object uses to determine whether two objects are the same.