Single-agent and simultaneous-update contrarian majority dynamics both violate detailed balance and produce nonequilibrium steady states with non-vanishing flux, establishing the model as intrinsically irreversible rather than equilibrium with added noise.
Consider the closed three-configuration cycle R5 = (+,−,−)→R 2 = (+,+,−)→R 8 = (−,−,−)→R 5
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Contrarian Majority Dynamics: Violation of Detailed Balance and Nonequilibrium Steady States
Single-agent and simultaneous-update contrarian majority dynamics both violate detailed balance and produce nonequilibrium steady states with non-vanishing flux, establishing the model as intrinsically irreversible rather than equilibrium with added noise.