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Both cellular automata (CA) and lattice-gas automata (LG) provide finitealgorithmic presentations for certain classes of infinite dynamical systemsstudied by symbolic dynamics; it is customary to use the term `cellularautomaton' or `lattice gas' for the dynamic system itself as well as for itspresentation. The two kinds of presentation share many traits but also displayprofound differences on issues ranging from decidability to modelingconvenience and physical implementability.  Following a conjecture by Toffoli and Margolus, it had been proved by Kari(and by Durand--Lose for more than two dimensions) that any invertible CA canbe rewritten as an LG (with a possibly much more complex ``unit cell''). Butuntil now it was not known whether this is possible in general fornoninvertible CA--which comprise ``almost all'' CA and represent the bulk ofexamples in theory and applications. Even circumstantial evidence--whether infavor or against--was lacking.  Here, for noninvertible CA, (a) we prove that an LG presentation is out ofthe question for the vanishingly small class of surjective ones. We then turnour attention to all the rest--noninvertible and nonsurjective--which compriseall the typical ones, including Conway's `Game of Life'. For these (b) we proveby explicit construction that all the one-dimensional ones are representable asLG, and (c) we present and motivate the conjecture that this result extends toany number of dimensions.  The tradeoff between dissipation rate and structural complexity implied bythe above results have compelling implications for the thermodynamics ofcomputation at a microscopic scale.

When--and how--can a cellular automaton be rewritten as a lattice gas?