A novel power law was found above 65 K in the I-V characteristics of WiiSviC&CmOy single crystals with the magnetic field perpendicular to the c axis. At 80 K, the power-law exponent decreased sharply up to 1.5 T but remained nearly constant above it, suggesting an abrupt crossover to a different mechanism. An unusual field dependence of resistivity was also found, which cannot be explained by simple flux-flow theory. The above novel features of the Lorentz-force-independent dissipation can be consistently explained by a model based on two-dimensional vortex-antivortex pair breaking. PACS numbers: 74.40.+k, 74.60.Ge It has been recognized that highly anisotropic high-T c oxides show Lorentz-force-independent energy dissipation in the mixed state. This phenomenon has been reported for La-Sr-Cu-O [1], Bi 2 Sr 2 CaCu 2 0 > , [2], Y 2 Ba 4 Cu80,6 [3], and Tl-Ba-Ca-Cu-O [4,5]. A clear experiment performed by lye, Nakamura, and Tamegai [2] has shown that the resistivity in the a -b plane does not change when the applied magnetic field is rotated within the plane. This brought up serious questions as to whether flux creep or flux flow, which are driven by the Lorentz force, are truly the origin of dissipation. Although many theories to explain this Lorentz-force independence have been proposed [4,6-8], the mechanism of the dissipation has not yet become clear. In this Letter, we report the first observation of clear power-law current-voltage (I-V) characteristics in the Lorentz-force-independent dissipative state in Bi 2 Sr 2 CaC^Oy. The existence of a power law and the behavior of the power-law exponent give us clues to solve the origin of the dissipation. Studies focused on the KosterlitzThouless (KT) transition have revealed that high-7V oxides show power-law I-V characteristics in the vicinity of the mean-field transition temperature in zero magnetic field [9] or for a field applied parallel to the c axis [10-12]. At lower temperatures, nonlinear I-V characteristics are also observed for the field parallel to the c axis [13,14]. These are interpreted in terms of the vortex-glass superconductivity [13] or other mechanisms [14-16]. However, clear power-law I-V characteristics have not yet been reported for the case of the field perpendicular to the c axis, although lye, Nakamura, and Tamegai [2] reported a nonlinear relation between the current and the voltage.Most of the theories [4,6,7] to explain the Lorentzforce-independent dissipation predict flux-flow-or fluxcreep-type I-V characteristics, which means that the dissipation is Ohmic if the current density is sufficiently small. Therefore, our observation of power-law I-V characteristics in the Lorentz-force-independent dissipation imposes a significant restriction on the explanation of the dissipation mechanism. We also find an abrupt change in the magnetic-field dependence of the power-law exponent and the resistivity around 2 T. We interpret these observations by a novel model, which considers the vortex-antivortex pair breaking combined with the stiffness of th...