Path-Dependency describes a situation when the same position gets a different value depending on a sequence of moves by which it has been reached. Whilst a few programs do this by design , within the standard alpha-beta framework path-dependency is considered undesirable, if impossible to avoid.
- The position can be treated differently if there is a chance of repetition or hitting into a fifty-move rule.
- Different move ordering can cause different result (different moves causing a cutoff), when it comes from the hash table 
- Hf a program uses search extensions, search depth may be different (i.e. 1. d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.Nf3 vs 1.d4 Nf6 2.c4 e6 3.Nf3 Bb4+ 4.Nc3, where only the latter triggers a check extension)
- History-dependent heuristics, like some versions of LMR may prune different sub-trees.
- "Don't trust draw score" <=Is it true? by Teerapong Tovirat, CCC, August 08, 2001 » Repetitions, Graph History Interaction
- path dependent evaluation by Daniel Shawul, Winboard Forum, April 20, 2005
- Re: And a still unsolved test position by Uri Blass, CCC, June 09, 2005 » Movei
- Semi-Path Dependent Hashing: a semi-useless idea by Zach Wegner, CCC, May 24, 2008 » Transposition Table
- Repetitions/50 moves and TT by Sergei Markoff, CCC, September 13, 2011
- Texel recipe to fix TT draws scores by Marco Costalba, CCC, June 23, 2012 » Texel