 ‘Hidden variables’ approaches seek to explain quantum phenomena as equilibrium statistical effects arising from a deeper-level theory, rather strongly in analogy with attempts at understanding thermodynamics in terms of statistical mechanics (see the entry on  philosophy of statistical mechanics).  Of these, the most developed are the so-called pilot-wave theories, in particular the theory by de Broglie and Bohm (see also the entry on  Bohmian mechanics).  Pilot-wave theories are no-collapse formulations of quantum mechanics that assign to the wave function the role of determining the evolution of (‘piloting’, ‘guiding’) the variables characterising the system, say particle configurations, as in de Broglie’s (1928) and Bohm’s (1952) theory, or fermion number density, as in Bell’s (1987, Chapter 19) ‘beable’ quantum field theory, or again field configurations, as in various proposals for pilot-wave quantum field theories (for a recent survey, see Struyve 2011).