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We present an efficient sampling method for computing a partition functionand accelerating configuration sampling. The method performs a random walk inthe $\lambda$ space, with $\lambda$ being any thermodynamic variable thatcharacterizes a canonical ensemble such as the reciprocal temperature $\beta$or any variable that the Hamiltonian explicitly depends on. The partitionfunction is determined by minimizing the difference of the thermal conjugatesof $\lambda$ (the energy in the case of $\lambda=\beta$), defined as thedifference between the value from the dynamically updated derivatives of thepartition function and the value directly measured from simulation.Higher-order derivatives of the partition function are included to enhance theBrownian motion in the $\lambda$ space. The method is much less sensitive tothe system size, and the size of $\lambda$ window than other methods. On thetwo dimensional Ising model, it is shown that the method asymptoticallyconverges the partition function, and the error of the logarithm of thepartition function is much smaller than the algorithm using the Wang-Landaurecursive scheme. The method is also applied to off-lattice model proteins, the$AB$ models, in which cases many low energy states are found in differentmodels.

Enhanced sampling in generalized ensemble with large gap of sampling parameter: case study in temperature space random walk