Thermodynamic RAM (kT-RAM) is a neuromemristive co-processor design based on the theory of AHaH Computing and implemented via CMOS and memristors. The co-processor is a 2-D array of differential memristor pairs (synapses) that can be selectively coupled together (neurons) via the digital bit addressing of the underlying CMOS RAM circuitry. The chip is designed to plug into existing digital computers and be interacted with via a simple instruction set. Anti-Hebbian and Hebbian (AHaH) computing forms the theoretical framework from which a nature-inspired type of computing architecture is built where, unlike von Neumann architectures, memory and processor are physically combined for synaptic operations. Through exploitation of AHaH attractor states, memristor-based circuits converge to attractor basins that represents machine learning solutions such as unsupervised feature learning, supervised classification and anomaly detection. Because kT-RAM eliminates the need to shuttle bits back and forth between memory and processor and can operate at very low voltage levels, it can significantly surpass CPU, GPU, and FPGA performance for synaptic integration and learning operations. Here, we present a memristor technology developed for use in kT-RAM, in particular bi-directional incremental adaptation of conductance via short low-voltage 1.0 V, 1.0 microsecond pulses.