Extended Data Fig. 1: Conceptual energy landscape for computation and reset.

a, Free energy states of a reusable molecular system. When the system is recharged, it will remain in a local energy minimum (state 2) until an input becomes present. As a catalyst, the input reduces the kinetic barrier and creates a smoother pathway for producing the desired output while reaching a lower energy state that is another local minimum (state 3). After computing the input-output function, the system will remain in the local minimum that has a higher free energy than the equilibrium state of global minimum (state 4). When heat is applied, the system will transition to a denatured state with a free energy higher than any other states (state 1). When heat is removed (cooling applied), the system will return to the recharged state if the input is absent or the output state if the input is present. b, Multiple output states for computing distinct input-output functions. Each input will reduce the kinetic barrier for reaching a specific output state. Heat will bring the system to the same denatured state regardless of the output state, and cooling will allow the system to return to the same recharged state when the input is absent. c, DNA implementation of a reusable molecular system with two output states. The denatured state involves eight single strands, two of which fold into two hairpins in the recharged state, four form two duplexes, and the other two remain single-stranded. Compared to the denatured state, the recharged state has two fewer separated molecules (lower entropy) but substantially more base pairs (lower enthalpy), resulting in a lower energy state. One of the two possible output states is illustrated as state 3, where a hairpin unfolds and becomes bound to two other strands, separating a duplex. Compared to the recharged state, the output state has one fewer separated molecules but 7 more base pairs. With sufficiently high concentration, the gain in enthalpy will exceed the loss in entropy and result in a lower energy state. The unfolding of the hairpin also comes with a gain in entropy, contributing to the lower energy state. The equilibrium state has both hairpins unfolded and each converted to a three-stranded complex, doubling the energy difference between the recharged and the output state.