The cross-field plasma diffusion coefficient is expressed in terms of the perturbed potential energy W by making use of the nonlinearity of orbit diffusion. The thermodynamic bound of the energy W for a current-carrying collisionless plasma has been determined consistently with four constraints: the invariance of averaged Hamiltonian, angular momentum, entropy and density. It is found that with momentum invariance the major contribution from the plasma current cancels, and the lowest upper bound of W is determined by the high-order toroidal effect coupled with the plasma current, which yields the neo-Alcator (TFTR) scaling for the energy confinement time. When neoclassical deformation is allowed in the plasma distribution, the thermodynamic bound has additional terms which come from the neoclassical source of free energy due to the bootstrap current. When the poloidal beta is larger than a certain critical value, the energy confinement time shows the effect of density saturation, and becomes proportional to the plasma current.