Alexei V. Tkachenko

The quantum measurement problem, i.e., the apparent conflict between unitary quantum evolution and non-unitary, stochastic wave-function collapse, remains unresolved a century after the formulation of quantum mechanics. We first review the standard picture, from the Copenhagen prescription with its Heisenberg cut, through von Neumann’s movable cut, to environment-induced decoherence, which explains the emergence of stable classical records but still presupposes the Born rule and therefore cannot by itself replace the measurement postulates. We then connect this problem to the Maximum Entropy Principle in two complementary ways. First, decoherence drives the measurement apparatus toward the least biased state compatible with the dynamically protected pointer distribution, so that the emergent collapse may be viewed as a thermodynamic relaxation toward constrained maximum entropy. Second, we propose a Timeless Histories formulation of quantum mechanics in which the primitive objects are ordered sequences of events rather than evolving wave functions. Their conditional probabilities are assigned, relative to specified refinements, by a single Born–Boltzmann rule that combines the quadratic structure of Born’s rule with Boltzmann’s counting of equally probable microstates. The textbook form of Born’s rule, the projection postulate, density operators, and wave functions are then recovered as derived informational constructs, while collapse becomes Bayesian conditioning on recorded events. Time and space enter only subsequently through unitary translation symmetry. Since the probability rule is postulated without reference to any physical collapse or classical observer, the usual circularity of the decoherence program is avoided. Decoherence can then be invoked to explain the stability and approximate additivity of macroscopic records, i.e., the emergence of classicality.

We present a framework for chemical learning based on competitive dimerization networks (CDNs)---systems in which multiple molecular species, e.g., proteins or DNA-RNA oligomers, reversibly bind to form dimers. We show numerically that these networks can, in principle, be trained in vitro through directed evolution, enabling the implementation of complex learning tasks such as multiclass classification without digital hardware or prior knowledge of all microscopic association constants. Each molecular species functions analogously to a neuron, with binding affinities acting as tunable synaptic weights. A training protocol involving mutation, selection, and amplification of DNA-based components allows CDNs to robustly discriminate among noisy input patterns. The resulting classifiers exhibit strong output contrast and high mutual information between input and output, especially when guided by a contrast-enhancing loss function. Comparative analysis with in silico gradient descent training reveals closely correlated performance. These results establish CDNs as a promising platform for analog physical computation, bridging synthetic biology and machine learning, and advancing the development of adaptive, energy-efficient molecular computing systems.

A minimal model of ionic aggregation in concentrated ZnCl 2 is developed, guided by molecular dynamics simulations with a machine-learned potential. It explicitly incorporates solvent-site depletion, correlated chloride binding, and allows for loops within Zn–Cl clusters. Dehydration drives two coordination-controlled structural changes: a crossover at Z = 2 from predominantly isolated Zn-containing species to Cl-bridged clusters and the onset of gelation near Z ≈ 3 . The model reproduces the concentration-dependent trends observed in the molecular dynamics simulations with two fitted parameters, while the cluster-size distribution at the highest concentration is consistent with three-dimensional percolation scaling over the accessible range of cluster sizes.

Mitochondria are central hubs of cellular bioenergetics, converting chemical free energy into ATP while inevitably dissipating heat during respiration. Fluorescence-based thermometry has been interpreted as evidence for intracellular “hot spots” more than 10 °C above bulk physiological temperature, implying that mitochondria might operate far outside conventional thermal bounds. Yet such large gradients are difficult to reconcile with mitochondrial size, aqueous thermal conductivity, and limited metabolic power. Beyond passive heat diffusion, a remaining question is whether nonequilibrium biochemical processes, including respiration-driven proton pumping, could actively maintain local temperature gradients as nanoscale heat pumps. Here, we establish a model-independent thermodynamic bound based only on the Second Law. Applied to the inner mitochondrial membrane, this bound limits the temperature difference that any biochemically driven mechanism could sustain, even under perfect efficiency and maximal power. The resulting upper limit is a small fraction of a degree, ruling out multidegree mitochondrial overheating.

Mitochondria are central hubs of cellular bioenergetics, converting chemical free energy into ATP while inevitably releasing heat during respiration. Fluorescence-based thermometry has been interpreted to show intracellular “hot spots” more than 10 °C above the bulk physiological temperature, implying that mitochondria might operate far outside conventional thermal bounds. Such claims, however, appear inconsistent with basic biophysics: the small size of mitochondria, their aqueous and highly conductive environment, and their limited power output all argue against large steady-state temperature gradients. This discrepancy has prompted renewed scrutiny of both the physical limits of intracellular heat transfer and the biological interpretation of nanoscale thermal measurements. A key open question is whether nonequilibrium biochemical processes, such as respiration-driven proton pumping, could act as nanoscale heat pumps that maintain higher local temperatures than allowed by passive diffusion alone. Here, we develop a model-independent thermodynamic analysis based solely on the Second Law of Thermodynamics to bound the maximal temperature difference that any biochemically driven mechanism can sustain across the inner mitochondrial membrane and show that even under idealized conditions the achievable temperature rise is restricted to a small fraction of a degree, effectively closing this loophole.

Programmable self-assembly enables the construction of complex molecular, supramolecular, and crystalline architectures from well-designed building blocks. We introduce a hypergraph-based formalism, Blocks & Bonds (B&B), which generalizes classical chemical graph theory by incorporating directed and multicolored interactions, internal symmetries, and hierarchical organization. Within this framework, we develop the Structure Code (SC), a compact and versatile language for describing self-assembled architectures. We define a Kolmogorov-style structural complexity as the total information content of SC, obtained through its tokenization and Shannon information assignment. Complementing this encoding-based measure, we introduce a much simpler quantity, the compositional complexity, which depends only on the number and cumulative usage of block and bond types in the construction set. A central result of this work is a strong empirical correlation between the token-based structural complexity and the compositional complexity across all examined systems. Owing to this agreement, the compositional complexity emerges as the most practical and broadly applicable measure: it is easy to compute, requires no explicit encoding, and yet closely tracks the actual information content of structurally diverse architectures. Applications to molecular systems (ethylene glycol and glucose), DNA-origami lattices, and crystalline assemblies show that B&B hypergraphs provide a unified, scalable, and information-efficient representation of structural organization, naturally capturing symmetry, modularity, and stereochemistry. This framework establishes a quantitative foundation for complexity-aware classification and inverse design of programmable matter.

We present a novel framework for chemical learning based on Com- petitive Dimerization Networks (CDNs)— systems in which multiple molecular species, e.g. proteins or DNA/RNA oligomers, reversibly bind to form dimers. We show that these networks can be trained in vitro through directed evolution, enabling the implementation of complex learning tasks such as multiclass classification without digital hardware or explicit parameter tuning. Each molecular species functions analogously to a neuron, with binding affinities acting as tunable synaptic weights. A training protocol involving mutation, selection, and amplification of DNA-based components allows CDNs to robustly discriminate among noisy input patterns. The resulting classifiers exhibit strong output contrast and high mutual information between input and output, especially when guided by a contrastenhancing loss function. Comparative analysis with in silico gradient descent training reveals closely correlated performance. These results establish CDNs as a promising platform for analog physical computation, bridging synthetic biology and machine learning, and advancing the development of adaptive, energy-efficient molecular computing systems. Significance Statement This study introduces a new paradigm for learning based on chemical reaction networks rather than digital circuits. Using Competitive Dimerization Networks (CDNs)—biomolecular systems in which species reversibly bind to form dimers—complex classification tasks are learned through in vitro directed evolution. This approach eliminates the need for digital hardware or gradient-based optimization, relying instead on intrinsic molecular dynamics for computation. The resulting chemical classifiers achieve high fidelity and robustness to noise, with performance comparable to that of gradient descent training. These findings establish CDNs as a scalable, energy-efficient platform for molecular computing, suggesting broad potential applications in diagnostics, biosensing, synthetic biology, and nanotechnology, where programmable, adaptive chemical systems could serve as alternatives to conventional electronic processors.