Spike timing is a regime choice, and regimes have a thermodynamic bill

What the work claims

This is a simulation study in circuit physics, not a hardware measurement, and it says so. The authors take an ultra-low-power analog spiking neuron designed in 65 nm CMOS, a simplified Morris-Lecar style circuit previously published as a 4-fJ-per-spike design, and subject it to industrial-grade transient noise SPICE simulation, in which every transistor carries its own state-dependent physical noise source from the foundry compact model¹. Their first claim is qualitative replication of the classical neuroscience experiments: under a constant supra-threshold current the CMOS neuron behaves like a self-running oscillator whose spike times accumulate jitter, while under a frozen filtered white-noise input sitting on a sub-threshold DC component each spike is an event triggered by a state transition, and the jitter largely vanishes. Their second claim is quantitative: the accumulated jitter in the oscillatory regime is dominated by white thermal transistor noise, grows linearly with spike count, and obeys a thermodynamic uncertainty relation that prices precision in units of dissipated energy, with the simulated neuron sitting about a factor of 25 above that fundamental floor.

How it works

The two regimes differ in what a spike is. In the oscillatory regime, a constant 20 pA drive makes the neuron fire repetitively with a mean inter-spike interval of about 32 microseconds, and each cycle adds independent phase noise, like a free-running clock. The authors estimate the intrinsic noise floor at about 0.7 mV standard deviation from the square root of kT over C, against a membrane swing of 0 to nearly 200 mV at a 200 mV supply, so fluctuations are just under 1 percent. Over 1000 simulated trials the variance of the n-th spike time relative to the first grows as n minus 1 times the period jitter, the signature of white, time-decorrelated noise, with a slight deviation from linearity beyond about 25 spikes that they attribute to 1/f noise. In the excitability regime the DC component, 5 pA, sits below the 7 pA threshold, and the neuron fires only when a fluctuation of the frozen filtered input, standard deviation 20 pA filtered with a 5 microsecond time constant, pushes it over. Each spike is then a discrete state transition rather than one more turn of an oscillator, and the input's fluctuating, resetting action prevents phase-error accumulation. Almost all spikes align across trials; the exceptions, the 4th and 15th spikes of the particular input used, are flagged as outliers with variances of 20 and 8 microseconds squared, moments where the transition itself is noise-triggered.

The thermodynamic part is what elevates this beyond a replication. A thermodynamic uncertainty relation applies to overdamped Markovian systems at steady state and states that the relative variance of any time-integrated current-like observable cannot fall below twice kT divided by the expected dissipated energy. Applied to the spike frequency of the oscillatory neuron, with a measured dissipation of about 1 femtojoule per spike cycle at 20 pA, the bound reads 2.6 x 10^-10 seconds divided by the observation time. The simulated jitter, 2 x 10^-4 divided by n minus 1 with the time base of 32 microseconds per cycle, lands a factor of 25 above that floor: the neuron is close to, but not at, its thermodynamic limit. Crucially, the authors note the bound does not apply to the excitability regime, because there spiking is a non-stationary process. In their words, the physical limitations the oscillatory regime suffers under thermodynamics are alleviated in the excitability regime.

Where a skeptic should push

The most load-bearing assumption is that foundry-grade simulation of one 65 nm design generalizes to other analog neurons and, more ambitiously, to biological ones. The authors are careful: they state that transistor-to-transistor variability in low-frequency noise magnitude makes them question the universality of the clean white-noise linear accumulation law they observed, and they describe the study as preliminary, with the underlying dynamics to be modeled in future work. There are no silicon measurements here, and no biological validation; the bridge to Mainen and Sejnowski is qualitative resemblance of raster plots, not a fitted model.

Second, the comparison between the measured jitter and the thermodynamic bound is explicitly approximate: the variance of spike-time differences and the variance of the empirical frequency are not the same object, and the authors say so while using one as a proxy for the other. The factor-of-25 figure therefore carries model-proxy slippage, and the 1 fJ-per-cycle dissipation number inherits the supply-current integration over one cycle from the same simulation framework. Third, the frozen-noise protocol is an idealization: real inputs are not replayed, so the reliability advantage of the excitability regime in the paper depends on the input itself carrying the information, which is precisely the coding question at stake. Accept the core physics, it is solid stochastic thermodynamics applied carefully; treat the specific numbers as design-point illustrations rather than universal constants.

Coding regime as the reliability budget of wetware

The non-obvious implication for organoid intelligence is that spike-time reliability is a choice of operating regime, not a fixed property of the substrate, and the choice is made by whoever designs the stimulation, whether they know it or not. A culture driven into persistent self-sustained activity, by tonic excitation, by a high-conductance state, or by an epileptiform tendency no one has corrected, is in the oscillator regime of this paper: each spike inherits accumulated phase noise, so any computation that assumes precise relative spike times is quietly degraded in proportion to how long the oscillation has been running. The same culture held near threshold and driven by structured, fluctuating input is in the excitability regime, where the input itself resets the timing error on every event and precise temporal codes become physically achievable. The classic Mainen and Sejnowski result was always cited as evidence that biology uses an event-based code; this paper adds the engineering corollary that the code is reliable because of the regime, and the regime is settable.

There is also a floor, and it is substrate-agnostic. The thermodynamic uncertainty relation applies to any overdamped dissipative stochastic dynamical system, a category the authors explicitly note includes biological neurons. Precision in a steady-state process costs dissipated energy, full stop. For biological computing this reframes an old intuition: living tissue is noisy, so its computations must be average-based and timing-insensitive. That is true for oscillatory, rate-coded operation. But the excitability result shows the floor can be sidestepped rather than paid, by moving the computation into event-triggered transitions. The dissipation numbers are also a useful calibration point: the CMOS neuron dissipates about 1 femtojoule per spike cycle, while biological spikes cost picojoules. Per unit of energy the analog device has orders of magnitude more headroom against the bound than tissue does, which is one more way of saying the energetic-efficiency argument for organoid computing has to be made in terms of what the tissue computes, not how cheaply it spikes.

The threats are concrete. Closed-loop OI rigs that deliver stimulation with a large tonic component are pushing their substrate toward the oscillator regime, maximizing exactly the jitter accumulation this paper quantifies, and then reading out the result with temporal decoders. Anyone building a DishBrain-style system on precise spike-time credit assignment should treat this as a measurement obligation: quantify phase-noise accumulation in the driven culture before trusting the timing channel. On the analog side, the 1/f deviation and device-to-device variability the authors flag are a reminder that front-end electronics have the same disease in slower form, so noise budgets for a wetware system must cover the electrode and the tissue in the same analysis. The opportunity is equally concrete: the paper's closing suggestion, that a fluctuating input could be the solution to an optimal control problem minimizing jitter and energy at once, is essentially a design spec for a stimulation encoder for living computers, and it is testable on a multielectrode array within existing closed-loop infrastructure.

The bottom line

Established: with foundry-grade noise simulation, a 65 nm analog spiking neuron reproduces the constant-versus-fluctuating-input reliability contrast first shown in biological neurons; jitter in the oscillatory regime accumulates linearly and is dominated by white thermal noise; and a thermodynamic uncertainty relation bounds that regime's precision at about 2.6 x 10^-10 seconds over the observation time, with the simulated neuron a factor of 25 above the floor at roughly 1 femtojoule dissipated per cycle. Established also, by the authors' own analysis: the bound does not apply to the excitability regime, where event-triggered spiking resets timing error. Open: silicon validation of the predicted jitter statistics, the role of 1/f noise and device variability, and whether the excitability regime's advantage survives non-frozen, information-carrying inputs. What would strengthen the case: measured jitter accumulation on fabricated chips matching the simulated linear law. What would complicate it: dominant low-frequency noise erasing the clean white-noise scaling, which would push real devices further from the bound and make timing precision even more expensive than simulated. For organoid computing, the actionable rule is simple: decide which regime your culture is in before you decide what code to read out.