Dynamical systems that evolve unidirectionally with respect to time provide a natural mechanism for implementing a time-domain, near-zero-threshold energy rectifier. In this paper we implement such a dynamical system using a pair of differential, leaky floating-gates and demonstrate that the circuit can sense and record signals of interest while compensating for environmental variations. A Fowler-Nordheim (FN) tunneling current has been used to implement the leakage process, which we experimentally show can be modulated by signals at energy levels below femtojoules. At this level of energy, the proposed FN-system could be self-powered using different types of biopotential energy sources like intra-cellular potentials, a feature that was not possible with previously reported recorders. Furthermore, the degree of modulation is shown to be a function of the input intensity as well as time-of-occurrence, which opens up the possibility of using reconstruction techniques to reconstruct the input signal from measurement of multiple sensing devices. Using devices fabricated in a 0.5 μm standard CMOS process, we demonstrate recording of 6 mV events with retention capability lasting over 30 minutes.