The Minoan and Mycenean "Linear" writing system was a relatively conservative one. I mean, the same signs (with a similar form and identical value) were used with little change over over several centuries. Yet one cannot deny the changes that happened to the script during its adaptation by mainland Greek cities and their few literate individuals.
The Mycenean Linear B script is essentially the same as the (somewhat earlier) Linear A one. The only important differences are (apart from rounding or simplification of some signs) the emergence of a handful of "new" syllabary signs, that cannot be found in any Linear A document (almost all Linear A signs continued to see some use in Linear B, but the reverse is not true).
First, what are these signs? If one examines thoroughly, the following ones can be added to the list: 'JO', 'QO', 'PTE', 'DWO', 'DWE', 'TWO', 'TWE', etc.
I intentionally did not add 'NO', 'DO' and 'WE' because these are not necessarily new - and some instances of these signs may well hide under not-well categorized Linear A signs. For example, Lin A *28 may be an ill-concieved grouping of three different signs: 'I', 'AI' or 'NO' and Lin A *53 may contain examples of both 'RI' and 'WE'.
From the remaining "surely new" ones, one can find examples of newly invented signs. The best example is Lin B *32 = 'QO'. If one examines the structure of this sign, there can be no doubts, that it stood for "cow" or "bull", that appears to derive from archaic Greek *QOUS, as Miguel Valerio has already pointed out in his article.
So new signs were readily invented, there can be no doubt about that. But some signs seem to evolved on a more complex path. One example is the sign Lin B *36 = 'JO' , that has no clear origin in Greek and might be a "transformed" descendant (i.e. in both form and/or phonetic value) of Linear A *301, whose value is unknown, but seems to terminate with -U rather than -O. But a far more brilliant example is the case of "librum" signs, as I will explain below.
It was already discovered by some, that the symmetric form of the Linear B *90 (='DWO') sign does have something to do with its phonetic value. Since *DWO would have meant "two" in Mycenean Greek, Miguel Valerio has theorized that this special sign would have arisen from the unification of two Lin B *42 (='WO') signs. While this theory is attractive, there are serious problems. First: why would a scribe replicate a 'WO' sign? The only plausible reason would be if this sign would have meant 'one', but this is highly unlikely. We know that the numeral "one" did not begin with 'WO' in the Mycenean language. And there is not a single convincing instance of using the 'WO' sign as a numeral.
To bridge these inconsistences and to amend the theory, I would propose a slightly different version that builds on the previous hypothesis (namely, that 'DWO' indeed intended to stand for 'two') and explain where the form of Lin B *90 came from. You can see the basic elements of this theory on the figure below.
Basically, if we align the Lin A signs with their Lin B counterparts, we will have 2 Lin B symbols (*90 and *83) with only one possible ancestral Lin A sign (*118). Since we know that the sign Lin B *90 contains an invention, regarding its phonetic value, it is possible that this novel phonetic value simply represents a Greek translation of its original Minoan meaning. But how did we get "two" from an image depicting a "two-armed librum" ?
This is not impossible, since a (compound) word for a "two-armed librum" may carry the particle 'two' at its very beginning, and can thus be abbreviated (during the formation of the acrophonic script) with the word "two" (remember, numerals for small quantities tend to be short in almost every language around the world).
The other sign that likely descends from the Lin A *118 ('librum') sign is Lin B *83, whose reading is - unfortunately - unknown. What we can make out of the context of Lin B *83, is that it probably has -I as a vowel part (it tends to be followed by J- series signs). For the consonantal part, no one can be sure, but if this theory is correct - and Lin A *118 & Lin B *83 share the same phonetic value, then the relatively high frequency fo Lin A *118 in texts suggests it carries a 'simple' consonant instead of a derived one (i.e. not DW-, TW-, SW-, RY- or like). Since there is only one case of a yet-unassigned I-series simple syllabary sign, I tentatively assigned Lin A *118 / Lin B *83 the value ZI, but of course if any of you could bring up a better solution, I would grateful to hear it.
Does this kind of development sound familiar to either one of you?
The mentioned case is fairly similar to that of the Japanese Kanji characters, with their On'yomi reading (phonetic) contrasted to the Kun'yomi reading (ideogrammatic). The only real difference is that we now have two slightly different signs for each type of reading. And - of course - both signs have eventually been fixed as purely phonetic ones.