The (non-)Gibbsian nature of states invariant under stochastic transformations

We investigate the Gibbsian nature of systems that are invariant under some stochastic transformation. A prime example concerns stationary measures for interacting particle systems. We bring together various types of results concerning the possible existence of effective Hamiltonians for nonequilibrium steady states using entropy techniques and large deviation estimates.

[1]  Roelof Kuik,et al.  From PCA's to equilibrium systems and back , 1989 .

[2]  T. Liggett.  Interacting Particle Systems , 1985 .

[3]  H. Künsch,et al.  Non reversible stationary measures for infinite interacting particle systems , 1984 .

[4]  Garrido,et al.  Effective Hamiltonian description of nonequilibrium spin systems. , 1989, Physical review letters.

[5]  N. B. Vasilyev.  Bernoulli and Markov stationary measures in discrete local interactions , 1978 .

[6]  W. Sullivan.  Potentials for almost Markovian random fields , 1973 .

[7]  The interaction potential of the stationary measure of a high‐noise spinflip process , 1993 .

[8]  M. Zahradník,et al.  ON ENTROPIC REPULSION IN LOW TEMPERATURE ISING MODELS , 1993 .

[9]  R. Schonmann.  Projections of Gibbs measures may be non-Gibbsian , 1989 .

[10]  J. Lebowitz,et al.  Statistical mechanics of probabilistic cellular automata , 1990 .

[11]  R. Holley,et al.  Free energy in a Markovian model of a lattice spin system , 1971 .

[12]  R. Kuik,et al.  Entropy and global Markov properties , 1990 .

[13]  Hans-Otto Georgii,et al.  Gibbs Measures and Phase Transitions , 1988 .

[14]  Roberto H. Schonmann,et al.  Pseudo-free energies and large deviations for non gibbsian FKG measures , 1988 .

[15]  Senya Shlosman,et al.  When is an interacting particle system ergodic? , 1993 .

[16]  A. Sokal,et al.  Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory , 1991, hep-lat/9210032.

[17]  Defining relative energies for the projected ising measure , 1992 .

[18]  Grinstein,et al.  Statistical mechanics of probabilistic cellular automata. , 1985, Physical review letters.