Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical Mechanics of Surjective Cellular Automata   Reversible cellular automata are seen as microscopic physical models, and
their states of macroscopic equilibrium are described using invariant
probability measures. We establish a connection between the invariance of Gibbs
measures and the conservation of additive quantities in surjective cellular
automata. Namely, we show that the simplex of shift-invariant Gibbs measures
associated to a Hamiltonian is invariant under a surjective cellular automaton
if and only if the cellular automaton conserves the Hamiltonian. A special case
is the (well-known) invariance of the uniform Bernoulli measure under
surjective cellular automata, which corresponds to the conservation of the
trivial Hamiltonian. As an application, we obtain results indicating the lack
of (non-trivial) Gibbs or Markov invariant measures for "sufficiently chaotic"
cellular automata. We discuss the relevance of the randomization property of
algebraic cellular automata to the problem of approach to macroscopic
equilibrium, and pose several open questions.
  As an aside, a shift-invariant pre-image of a Gibbs measure under a
pre-injective factor map between shifts of finite type turns out to be always a
Gibbs measure. We provide a sufficient condition under which the image of a
Gibbs measure under a pre-injective factor map is not a Gibbs measure. We point
out a potential application of pre-injective factor maps as a tool in the study
of phase transitions in statistical mechanical models.

37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat