The energy cost of computation has emerged as a central challenge at the intersection of physics and computer science. Recent advances in statistical physics—particularly in stochastic thermodynamics—enable precise characterizations of work, heat, and entropy production in information-processing systems driven far from equilibrium by time-dependent control protocols. A key open question is then how to design protocols that minimize thermodynamic cost while ensuring correct outcomes. To this end, we develop a unified framework to identify optimal protocols using fluctuation-response relations (FRRs) and machine learning. Unlike previous approaches that optimize either distributions or protocols separately, our method unifies both using FRR-derived gradients. Moreover, our method is based primarily on iteratively learning from sampled noisy trajectories, which is generally much easier than solving for the optimal protocol directly from a set of governing equations. We apply the framework to canonical examples—bit erasure in a double-well potential and translating harmonic traps—demonstrating how to construct loss functions that trade-off energy cost against task error. The framework extends trivially to underdamped systems, and we show this by optimizing a bit flip in an underdamped system. In all computations we test, the framework achieves the theoretically optimal protocol or achieves work costs comparable to relevant finite-time bounds. In short, the results provide principled strategies for designing thermodynamically efficient protocols in physical information-processing systems. Applications range from quantum gates robust under noise to energy-efficient control of chemical and synthetic biological networks.

Markedly increased computational power and data acquisition have led to growing interest in data-driven inverse dynamics problems. These seek to answer a fundamental question: What can we learn from time-series measurements of a complex dynamical system? For small systems interacting with external environments, the effective dynamics are inherently stochastic, making it crucial to properly manage noise in data. Here we explore this for systems obeying Langevin dynamics and, using currents, we construct a learning framework for stochastic modeling. Currents have recently gained attention for their role in bounding entropy production from thermodynamic uncertainty relations (TURs). We introduce a fundamental relationship between the cumulant currents there and standard machine-learning loss functions. Using this, we derive loss functions for several key thermodynamic functions directly from the system dynamics without the (common) intermediate step of deriving a TUR. These loss functions reproduce results derived both from TURs and other methods. More significantly, they open a path to discover new loss functions for previously inaccessible quantities. Notably, this includes access to per-trajectory entropy production, even if the observed system is driven far from its steady state. We also consider higher-order estimation. Our method is straightforward and unifies dynamic inference with recent approaches to entropy production estimation. Taken altogether, this reveals a deep connection between diffusion models in machine learning and entropy production estimation in stochastic thermodynamics.

We present implementations of two physically-embedded computation-universal logical operations using a 2-bit logical unit composed of coupled quantum flux parametrons—Josephson-junction superconducting circuits. To illustrate universality, we investigate NAND gates built from these two distinct elementary operations. On the one hand, Controlled Erasure (CE) is designed using fixed-point analysis and assumes that information must be stored in locally metastable distributions. On the other, Erasure-Flip (EF) leverages momentum as a computational resource and significantly outperforms the metastable approach, simultaneously achieving higher fidelity and faster computational speed without incurring any additional energetic cost. Notably, the momentum degree of freedom allows the EF to achieve universality by using both nontrivial reversible and irreversible logic simultaneously in different logical subspaces. These results not only provide a practical, high-performance protocol ripe for experimental realization but also underscore the broader potential of momentum-based computing paradigms.

Smartphones, laptops, and data centers are CMOS-based technologies that ushered our world into the information age of the 21st century. Despite notable advantages for scalable computing, CMOS implementations come with surprisingly large energetic costs. This challenge has revitalized scientific and engineering interest in energy-efficient information-processing designs. One current paradigm-dynamical computing-controls the location and shape of minima in potential energy landscapes that are connected to a thermal environment. The landscape supports distinguishable metastable energy minima that serve as a system's mesoscopic memory state. Information is represented by microstate distributions. Dynamically manipulating the memory states then corresponds to information processing. This framing provides a natural description of the associated thermodynamic transformations and required resources. Appealing to the bifurcation theory, a computational protocol in the metastable regime can be analyzed by tracking the evolution of fixed points in the state space. We illustrate the paradigm's capabilities by performing 1-bit and 2-bit computations with double-well and quadruple-well potentials, respectively. These illustrate how dynamical computing can serve as a basis for designing universal logic gates and investigating their out-of-equilibrium thermodynamic performance.

Reducing the energy inefficiency of conventional CMOS-based computing devices-which rely on logically irreversible gates to process information-remains both a fundamental engineering challenge and a practical social challenge of increasing importance. We extend an alternative computing paradigm that manipulates microstate distributions to store information in the metastable minima determined by an effective potential energy landscape. These minima serve as mesoscopic memories that are manipulated by a dynamic landscape to perform information processing. Central to our results is the control erase protocol, which controls the landscape's metastable minima to determine whether information is preserved or erased. Importantly, successive protocol executions can implement a NAND gate-a logically irreversible universal logic gate. We show how to practically implement CEs in a device created by two inductively coupled superconducting quantum interference devices (SQUIDs). We identify circuit parameter ranges that give rise to effective CEs and establish the device's robustness against thermally induced errors. These SQUID-based logical devices are capable of operating above GHz frequencies and at the kBT energy scale. Due to this, optimized devices and associated protocols provide a universal-computation substrate that is both computationally fast and energy efficient.

We implement a Szilard engine using a 2-bit logical unit consisting of inductively coupled quantum flux parametrons—Josephson-junction superconducting circuits with applications in both the classical and quantum information processing regimes. Detailed simulations show that it is highly thermodynamically efficient while functioning as a Maxwell demon—converting heat to work. The physically-calibrated design is targeted to direct experimental exploration. However, in realizing experiments variations in Josephson junction fabrication introduce asymmetries that result in energy inefficiency and low operational fidelity. We provide a design solution that mitigates these practical challenges. The resulting platform is ideally suited to probe the thermodynamic foundations of information processing devices far from equilibrium.

Alternative computing paradigms open the door to exploiting recent innovations in computational hardware to probe the fundamental thermodynamic limits of information processing. One such paradigm employs superconducting quantum interference devices (SQUIDs) to execute classical computations. This, though, requires constructing sufficiently complex superconducting circuits that support a suite of useful information processing tasks and storage operations, as well as understanding these circuits' energetics. First-principles circuit design leads to prohibitive algebraic complications when deriving the effective equations of motion-complications that to date have precluded achieving these goals, let alone doing so efficiently. We circumvent these complications by (i) specializing our class of circuits and physical operating regimes, (ii) synthesizing existing derivation techniques to suit these specializations, and (iii) implementing solution-finding optimizations which facilitate physically interpreting circuit degrees of freedom that respect physically grounded constraints. This leads to efficient and practical circuit prototyping, as well as accessing scalable circuit architectures. The analytical efficiency is demonstrated by reproducing the potential energy landscape generated by a SQUID. We then show how inductively coupling two SQUIDs produces a device that is capable of executing two-bit computations via its composite potential energy landscape. More generally, the synthesized methods detailed here provide a basis for constructing universal logic gates and investigating their thermodynamic performance.

Many have speculated whether nonequilibrium systems obey principles of maximum or minimum entropy production. In this work, we use stochastic thermodynamics to derive the condition for the minimum entropy production state (MEPS) for continuous-time Markov chains (CTMCs), even far from equilibrium. We show that real nonequilibrium steady states (NESS) generally violate both the MINEP and MAXEP principles. However, through numerical sampling of large interconnected CTMCs, we find that as system size increases, the steady-state entropy production tends to converge toward the minimum. This suggests that large nonequilibrium systems may self-organize to make efficient use of thermodynamic resources, offering a nuanced perspective on the longstanding debate between MAXEP and MINEP.

Entropy production (EP) is a central quantity in nonequilibrium physics as it monitors energy dissipation, irreversibility, and free energy differences during thermodynamic transformations. Estimating EP, however, is challenging both theoretically and experimentally due to limited access to the system dynamics. For overdamped Langevin dynamics and Markov jump processes it was recently proposed that, from thermodynamic uncertainty relations (TURs), short-time cumulant currents can be used to estimate EP without knowledge of the dynamics. Yet, estimation of EP in underdamped Langevin systems remains an active challenge. To address this, we derive a modified TUR that relates the statistics of two specific currents-one cumulant current and one stochastic current-to a system's EP. These two distinct but related currents are used to constrain EP in the modified TUR. One highlight is that there always exists a family of currents such that the uncertainty relations saturate, even for long-time averages and in nonsteady-state scenarios. Another is that our method only requires limited knowledge of the dynamics-specifically, the damping coefficient to mass ratio and the diffusion constant. This uncertainty relation allows estimating EP for both overdamped and underdamped Langevin dynamics. We validate the method numerically, through applications to several underdamped systems, to underscore the flexibility in obtaining EP in nonequilibrium Langevin systems.

Entropy production (EP) is a central quantity in nonequilibrium physics as it monitors energy dissipation, reversibility, and free energy differences during thermodynamic transformations. Estimating EP, however, is challenging both theoretically and experimentally due to limited access to the system dynamics. For overdamped Langevin dynamics and Markov jump processes it was recently proposed that, from thermodynamic uncertainty relations (TUR), short-time cumulant currents can be used to estimate EP without knowledge of the dynamics. Yet, estimation of EP in underdamped Langevin systems remains an active challenge. To address this, we derive a modified TUR that relates the statistics of two specific novel currents – one cumulant current and one stochastic current – to a system's EP. These two distinct but related currents are used to constrain EP in the modified TUR. One highlight is that there always exists a family of currents such that the uncertainty relations saturate, even for long-time averages and in nonsteady-state scenarios. Another is that our method only requires limited knowledge of the dynamics – specifically, the damping-coefficient to mass ratio and the diffusion constant. This uncertainty relation allows estimating EP for both overdamped and underdamped Langevin dynamics. We validate the method numerically, through applications to several underdamped systems, to underscore the flexibility in obtaining EP in nonequilibrium Langevin systems.

Alternative computing paradigms open the door to exploiting recent innovations in computational hardware to probe the fundamental thermodynamic limits of information processing. One such paradigm employs superconducting quantum interference devices (SQUIDs) to execute classical computations. This, though, requires constructing sufficiently complex superconducting circuits that support a suite of useful information processing tasks and storage operations, as well as understanding these circuits' energetics. First-principle circuit design, though, leads to prohibitive algebraic complications when deriving the effective equations of motion -- complications that to date have precluded achieving these goals, let alone doing so efficiently. We circumvent these complications by (i) specializing our class of circuits and physical operating regimes, (ii) synthesizing existing derivation techniques to suit these specializations, and (iii) implementing solution-finding optimizations which facilitate physically interpreting circuit degrees of freedom that respect physically-grounded constraints. This leads to efficient, practical circuit prototyping and access to scalable circuit architectures. The analytical efficiency is demonstrated by reproducing the potential energy landscape generated by the quantum flux parametron (QFP). We then show how inductively coupling two QFPs produces a device that is capable of executing 2-bit computations via its composite potential energy landscape. More generally, the synthesis methods detailed here provide a basis for constructing universal logic gates and investigating their thermodynamic performance.

We introduce a fast and highly-efficient physically-realizable bit swap. Employing readily available and scalable Josephson junction microtechnology, the design implements the recently introduced paradigm of momentum computing. Its nanosecond speeds and sub-Landauer thermodynamic efficiency arise from dynamically storing memory in momentum degrees of freedom. As such, during the swap, the microstate distribution is never near equilibrium and the memory-state dynamics fall far outside of stochastic thermodynamics that assumes detailed-balanced Markovian dynamics. The device implements a bit-swap operation -- a fundamental operation necessary to build reversible universal computing. Extensive, physically-calibrated simulations demonstrate that device performance is robust and that momentum computing can support thermodynamically-efficient, high-speed, large-scale general-purpose computing that circumvents Landauer's bound.

Thermodynamic uncertainty relations (TURs) express a fundamental lower bound on the precision (inverse scaled variance) of any thermodynamic charge-e.g., work or heat-by functionals of the average entropy production. Relying on purely variational arguments, we significantly extend TUR inequalities by incorporating and analyzing the impact of higher statistical cumulants of the entropy production itself within the general framework of time-symmetrically-controlled computation. We derive an exact expression for the charge that achieves the minimum scaled variance, for which the TUR bound tightens to an equality that we name the thermodynamic uncertainty theorem (TUT). Importantly, both the minimum scaled variance charge and the TUT are functionals of the stochastic entropy production, thus retaining the impact of its higher moments. In particular, our results show that, beyond the average, the entropy production distribution's higher moments have a significant effect on any charge's precision. This is made explicit via a thorough numerical analysis of "swap" and "reset" computations that quantitatively compares the TUT against previous generalized TURs.

Practical, useful computations are instantiated via physical processes. Information must be stored and updated within a system's configurations, whose energetics determine a computation's cost. To describe thermodynamic and biological information processing, a growing body of results embraces rate equations as the underlying mechanics of computation. Strictly applying these continuous-time stochastic Markov dynamics, however, precludes a universe of natural computing. Within this framework, operations as simple as a NOT gate (flipping a bit) and swapping two bits, and swapping bits are inaccessible. We show that expanding the toolset to continuous-time hidden Markov dynamics substantially removes the constraints, by allowing information to be stored in a system's latent states. We demonstrate this by simulating computations that are impossible to implement without hidden states. We design and analyze a thermodynamically costless bit flip, providing a counterexample to rate-equation modeling. We generalize this to a costless Fredkin gate—a key operation in reversible computing that is Turing complete (computation universal). Going beyond rate-equation dynamics is not only possible but also necessary if stochastic thermodynamics is to become part of the paradigm for physical information processing.

We analyze an engine whose working fluid consists of a single quantum particle, paralleling Szilard's construction of a classical single-particle engine. Following his resolution of Maxwell's Second Law paradox using the latter, which turned on physically instantiating the demon (control subsystem), the quantum engine's design mirrors the classically-chaotic Szilard Map that operates a thermodynamic cycle of measurement, thermal-energy extraction, and memory reset. Focusing on the thermodynamic costs to observe and control the particle and comparing these in the quantum and classical limits, we detail the thermodynamic tradeoffs behind Landauer's Principle for information-processing-induced thermodynamic dissipation in the quantum and classical regimes. In particular, and as found with the classical engine, we show that the sum of the thermodynamic costs over a cycle obeys a generalized Landauer Principle, exactly balancing energy extraction from the heat bath. Thus, the quantum engine obeys the Second Law. However, the quantum engine does so via substantially different mechanisms: classically measurement and erasure determine the thermodynamics, while in the quantum implementation the cost of partition insertion is key.

All computation is physically embedded. Reflecting this, a growing body of results embraces rate equations as the underlying mechanics of thermodynamic computation and biological information processing. Strictly applying the implied continuous-time Markov chains, however, excludes a universe of natural computing. We show that expanding the toolset to continuous-time hidden Markov chains substantially removes the constraints. The general point is made concrete by our analyzing two eminently-useful computations that are impossible to describe with a set of rate equations over the memory states. We design and analyze a thermodynamically-costless bit flip, providing a first counterexample to rate-equation modeling. We generalize this to a costless Fredkin gate---a key operation in reversible computing that is computation universal. Going beyond rate-equation dynamics is not only possible, but necessary if stochastic thermodynamics is to become part of the paradigm for physical information processing.

Szilard's now-famous single-molecule engine was only the first of three constructions he introduced in 1929 to resolve several challenges arising from Maxwell's demon paradox. Given that it has been thoroughly analyzed, we analyze Szilard's remaining two demon models. We show that the second one, though a markedly different implementation employing a population of distinct molecular species and semipermeable membranes, is informationally and thermodynamically equivalent to an ideal gas of the single-molecule engines. One concludes that (i) it reduces to a chaotic dynamical system-called the Szilard Map, a composite of three piecewise linear maps and associated thermodynamic transformations that implement measurement, control, and erasure; (ii) its transitory functioning as an engine that converts disorganized heat energy to work is governed by the Kolmogorov-Sinai entropy rate; (iii) the demon's minimum necessary "intelligence" for optimal functioning is given by the engine's statistical complexity; and (iv) its functioning saturates thermodynamic bounds and so it is a minimal, optimal implementation. We show that Szilard's third construction is rather different and addresses the fundamental issue raised by the first two: the link between entropy production and the measurement task required to implement either of his engines. The analysis gives insight into designing and implementing novel nanoscale information engines by investigating the relationships between the demon's memory, the nature of the "working fluid," and the thermodynamic costs of erasure and measurement.

11:20 – 11:40 Mapping the Operational Landscape of microRNAs in Synthetic Gene Circuits Tyler Quarton, Leonidas Bleris Bioengineering, The University of Texas at Dallas MicroRNAs are a class of short, noncoding RNAs that are ubiquitous modulators of gene expression, with roles in development, homeostasis, and disease. Engineered microRNAs are now frequently used as regulatory modules in synthetic biology. Moreover, synthetic gene circuits equipped with engineered microRNA targets with perfect complementarity to endogenous microRNAs establish an interface with the endogenous milieu at the single-cell level. The function of engineered microRNAs and sensor systems is typically optimized through extensive trial-and-error. Here, using a combination of synthetic biology experimentation in human embryonic kidney cells and quantitative analysis, we investigate the relationship between input genetic template abundance, microRNA concentration, and output under microRNA control. We provide a framework that employs the complete operational landscape of a synthetic gene circuit and enables the stepwise development of mathematical models. We derive a phenomenological model that recapitulates experimentally observed nonlinearities and contains features that provide insight into the microRNA function at various abundances. Our work facilitates the characterization and engineering of multi-component genetic circuits and specifically points to new insights on the operation of microRNAs as mediators of endogenous information and regulators of gene expression in synthetic biology.

Van der Waals heterostructures consisting of two-dimensional materials offer a platform to obtain materials by design and are very attractive owing to unique electronic states. Research on 2D van der Waals heterostructures (vdWH) has so far been focused on fabricating individually stacked atomically thin unary or binary crystals. Such systems include graphene, hexagonal boron nitride, and members of the transition metal dichalcogenide family. Here we present our experimental study of the optoelectronic properties of a naturally occurring vdWH, known as franckeite, which is a complex layered crystal composed of lead, tin, antimony, iron, and sulfur. We present here that thin film franckeite (60 nm < d < 100 nm) behaves as a narrow band gap semiconductor demonstrating a wide-band photoresponse. We have observed the band-edge transition at ∼1500 nm (∼830 meV) and high external quantum efficiency (EQE ≈ 3%) at room temperature. Laser-power-resolved and temperature-resolved photocurrent measurements reveal that the photocarrier generation and recombination are dominated by continuously distributed trap states within the band gap. To understand wavelength-resolved photocurrent, we also calculated the optical absorption properties via density functional theory. Finally, we have shown that the device has a fast photoresponse with a rise time as fast as ∼1 ms. Our study provides a fundamental understanding of the optoelectronic behavior in a complex naturally occurring vdWH, and may pave an avenue toward developing nanoscale optoelectronic devices with tailored properties.