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Chaos is usually referred to the sensitivity to initial conditions in whichthe nonlinearity plays a crucial role. Beyond such a mathematical description,the understanding of the underlying physical origin of the chaos is still notvery clear. Here we study the dissipative chaos from the perspective of thenonequilibrium dynamics. This was not fully investigated in the traditionalchaos theory, despite of the Lorenz's original discovery of chaos from thenonequilibrium atmosphere. We found that the nonequilibriumness as the degreeof detailed balance breaking can be quantified by the appearance of the steadystate probability flux in the state space. We uncovered that the dynamicalorigin of the onset and offset of the dissipative chaos such as Lorentzattractor is from the sudden appearance and disappearance of suchnonequilibrium flux. We also uncovered that the dissipation associated with theflux quantified by the entropy production rate gives the thermodynamical originof dissipative chaos. The sharp changes in the degree of nonequilibriumness bythe flux and the entropy production rate also provide alternative quantitativeindicators for the onset and offset of the dissipative chaos.

The dynamical and thermodynamical origin of dissipative chaos