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We study dissipative dynamics constructed by means of non-commutativeDirichlet forms for various lattice systems with multiparticle interactionsassociated to CCR algebras. We give a number of explicit examples of suchmodels. Using an idea of quasi-invariance of a state, we show how one canconstruct unitary representations of various groups. Moreover in models withlocally conserved quantities associated to an infinite lattice we show thatthere is no spectral gap and the corresponding dissipative dynamics decay toequilibrium polynomially in time.

Dissipative dynamics for infinite lattice systems