Papers

In classical anharmonic lattices, the resonance structure driving nonlinear mode mixing is reshaped by band gaps. However, it remains unclear whether a spectral gap hinders or promotes long-time thermalization. Here we study a dimerized Fermi-Pasta-Ulam-Tsingou chain - a classical SSH model analogue with alternating spring constants - and quantify how the acoustic-optical gap controls relaxation under alpha-type (cubic) nonlinearity. Tracking modal energies and spectral entropy via long-time symplectic simulations, we find a sharp isolation threshold when the dimerization strength reaches half its maximum value, set by the onset of the first umklapp process that allows two zone-boundary acoustic phonons to fuse into a zone-center optical phonon; below this threshold, three-wave acoustic-acoustic-optical scattering activates the optical branch on timescales of order 1e4 oscillation periods, while above it the bands remain dynamically isolated. We further show that boundary conditions reshape this picture, producing long-lived sticky states for specific mode excitations. These results establish the phononic gap as a tunable, momentum-selective filter for nonlinear energy transport, suggesting a general route to controlling thermalization in dimerized or topologically gapped nonlinear lattices.

We establish an exact equivalence between the fluctuations of integrated currents and the temporal statistics of current record events in continuous-time Markov jump processes. Specifically, we show that, under minimal assumptions, the Fano factor of an integrated current coincides exactly with the squared coefficient of variation of the inter-record waiting times. This result is obtained by showing that inter-record times induce a renewal structure, since each record event resets the system to a fixed state, and that their generating function can be expressed exactly in terms of a combinatorial organization governed by Narayana numbers. The equivalence extends previous results obtained for unicyclic networks to arbitrary finite-state graphs and provides a unified representation of current fluctuations in terms of record-time observables. The results are derived within a purely probabilistic framework and clarify the structural origin of current precision in terms of first-passage-like event statistics.

Prethermal states–long-lived quasi-equilibrium configurations–occur in a wide range of physical systems that exhibit fast dephasing or reconfiguration followed by slow relaxation towards thermal equilibrium. We experimentally studied the 1D interface between immiscible 2D Bose-Einstein condensates (BECs); following a quench, the interfacial capillary waves (ripplons) quickly relaxed into a long-lived prethermal state characterized by a persistent non-equipartition of energy, evoking the classic Fermi-Pasta-Ulam-Tsingou problem. We directly measured the interface's height profile as it evolved in time, identified the contribution of individual ripplon modes, and find that, though their individual amplitudes are thermally distributed, they are not in thermal equilibrium–high-momentum modes rapidly equilibrated with the bulk phonon modes of the 2D BEC, while lower momentum modes remained at elevated temperatures, forming a long-lived prethermal configuration for the whole system. We attribute this to kinematic isolation: the absence of energy- and momentum-conserving relaxation processes in our system at ultracold temperature.

Quantum reaction-transport systems consist of coherently propagating particles that irreversibly react upon encounter. Their relaxation is commonly classified as reaction-limited or transport-limited, depending on the relative timescales of reaction and particle transport. We show that this expectation fails in low dimensions by studying the quantum binary annihilation, $A+A \to \emptyset$, where reaction processes acquire singular fluctuation corrections below the upper critical dimension $D_c=2$. Consequently, fluctuations dominate the asymptotic kinetics for $D<2$. In one dimension, they render mean-field relaxation transient and drive the system toward a transport-limited regime with $n\sim t^{-1/2}$, governed by a quantum-Zeno scale even for arbitrarily weak loss. At $D=2$, the kinetics acquires logarithmic corrections, whereas above two dimensions mean-field scaling is asymptotically restored. At and below the upper critical dimension, mean-field behavior can nevertheless persist over parametrically long crossover times before the asymptotic fluctuation-dominated regime emerges. We also show that the same fluctuations generate effective elastic collisions despite the absence of microscopic coherent interactions. In $D>1$, these collisions redistribute momentum populations and are parametrically faster than losses in the transport-limited regime, allowing the system to approach a quasi-stationary thermal state.

Quantum states generated by generic time evolution are locally featureless: local measurements return random outcomes that are identical for all states. However, global snapshots in the computational basis are surprisingly effective at distinguishing between quantum states. We explore the ability of Bayesian classifiers to discriminate between many random quantum states using a small number of measurement outcomes. We identify a phase transition in the ability of the classifier to distinguish between $k$ candidate states with $m$ shots controlled by the variable $x = m / \ln k$, and derive the threshold value $x_c$. We extend our results to low-depth circuits near the onset of anti-concentration, as well as to noisy circuits and phase-random states.

We study Parrondo's paradox – the phenomenon where combining losing strategies yields a winning one – in a minimal discrete-time quantum walk. We introduce the transport vector, encoded in the coin's steady state, whose inner product with the initial coin state gives the walker's asymptotic velocity. More generally, the paradox emerges exactly when the transport vector of the combined strategy falls outside the cone spanned by the individual ones – a geometric criterion valid for any combination of strategies. It explains, for instance, why composing two coin operators within a single step can produce the paradox while simple alternation between them cannot, since alternation keeps the combined vector confined to the cone. The paradoxical set has nonzero measure, and we compute its probability explicitly in representative cases. This casts the paradox as one instance of designing reachable transport in quantum walks.

In June 2026, thousands of AI agents found that a small public wiki would accept edits from inside their sandboxes, and started using it to help one another pass a timed test. Each agent lived for about an hour and remembered nothing afterwards. Nobody asked them to cooperate, and the wiki had not been built for them. The complete record of what they wrote is public, and it is unusually informative, because it preserves not only what each agent wrote but what that agent could see before writing. We use it to follow the three decisions an agent had to make on arrival: where to write, what to call itself, and how to word its message. One rule governs all three. An agent takes an option with a probability close to the share of that option in what it can see, and the share that matters is the one on the page in front of it, then the one in the stream of recent edits, and only weakly anything older. Three minimal copying models, one per decision and with a single free parameter each, reproduce the heavy-tailed distribution of how many agents met on a page, the frequency of the pieces from which the agents built their names, and the patchwork of pages that are internally consistent and different from one another. Copying whatever the environment happens to show is enough to produce most of the collective structure of this population. It is also what makes such a population easy to steer, since whoever writes first, or writes while the others are quiet, sets the convention for everyone who comes later.

The Ballistic Macroscopic Fluctuation Theory (BMFT) is a path-integral based approach to treat large-scale correlations in interacting integrable systems which, so far, has only been applied to quasi-equilibrium settings. In this paper we extend this approach to integrable quench problems and, to illustrate it, we compute the time evolution of the full-counting-statistics (FCS) of a conserved charge. We identify the relevant path integral, solve it via saddle-point, and obtain a set of partial differential equations describing the dynamics of the FCS. We solve these equations explicitly for free fermionic systems and for the interacting cellular automaton Rule 54. In both cases, we recover the known exact results. For Rule 54, our construction moreover completes the solution across the entire ballistic window.

The range of intermolecular interactions plays a central role in determining the nature of phase behavior and critical phenomena. It is well established through studies of the Ising model that as interaction range increases, Monte Carlo simulations progressively approach meanfield predictions as the effects of critical fluctuations are suppressed. In this work, we investigate how varying interaction range influences fluid multicriticality using an interconverting lattice model that exhibits both Ising-like liquid-gas criticality and symmetric fluid tricriticality (similar to that in the superfluid $^4$He-$^3$He mixture). This minimal model serves as a representative system for exploring the evolution of competing critical points within a generic framework. We analyze the model using both meanfield theory and three-dimensional Monte Carlo simulations while systematically varying the number of interacting neighbors, $Z_n$, from 6 to 388. We find that the system with nearest-neighbor interactions ($Z_n=6$) reveals only two types of multicritical behavior, while for larger interaction ranges, four distinct archetypes emerge. We demonstrate the convergence of the simulation results to those of the meanfield theory as the number of interacting neighbors tends to infinity, and we discuss the results within the framework of crossover critical phenomena.

Two-dimensional massless Dirac systems, exemplified by graphene, are known to exhibit a divergent orbital diamagnetic susceptibility that scales linearly with system size. Motivated by viewing a chiral edge state as one half of an enlarged analogue of a benzene ring, we study Chern insulators under open boundary conditions and find the same divergent scaling. This giant diamagnetism is robust against disorder, revealing its topological nature. Our results further suggest a profound connection to the divergent diamagnetism of massless Dirac systems.

We develop a microscopic phase-space description of the quantum Calogero model in the presence of an external harmonic confining potential. Building on the quantum Lax-pair structure, we construct a Hermitian Wigner operator whose expectation value obeys the exact phase-space evolution equation d_t rho + lambda d_x rho - Omega^2 x d_lambda rho = 0 for arbitrary initial states and to all orders in the interaction strength. The resulting dynamics is a rigid rotation in phase space with period 2 pi/Omega, providing a microscopic realization of the isochronous dynamics of the trapped Calogero model. We further show that the moments of the phase-space density form rotating multiplets rather than independent conserved quantities. In particular, within the quadratic sector, the unique conserved combination is proportional to the trapped Hamiltonian, providing a nontrivial consistency check of the construction. In the limit Omega -> 0, the equation reduces to the exact free-streaming equation of the untrapped model.

We study stochastic and sharp restart in a one-dimensional lackadaisical discrete-time quantum walk with self-loop weight $\ell$. In the absence of restart, the dynamics has a flat band responsible for intrinsic localization and two dispersive bands supporting ballistic propagation. We compare two initially localized benchmark states: a flat-band-active state with finite flat-band overlap and a flat-band-dark state with zero flat-band overlap. For geometric stochastic restart with per-step restart probability $q$, the stationary mean-squared displacement scales as $q^{-2}$ as $q\to0$. In the same limit, the restart-site occupation probability approaches the restart-free intrinsic localized value for the flat-band-active state, whereas for the flat-band-dark state it vanishes as $q\ln(1/q)$. For power-law restart, where $p_m\propto m^{-s}$ is the probability that the waiting time to the next restart is $m$ steps, a normalized stationary site-occupation distribution exists only for $s>2$, while the stationary absolute spatial moment of order $p$ is finite only for $s>p+2$. In the regime $1<s\leq2$, at every fixed lattice site, the flat-band-active occupation converges to the intrinsic flat-band profile, while the flat-band-dark occupation tends to zero. We also consider monitored first detection with sharp restart, in which the walk is reinitialized after a fixed number $r$ of consecutive unsuccessful measurements. For fixed $r$, the mean first-detected-passage time of the flat-band-active state exhibits a minimum at an intermediate self-loop weight, whereas the flat-band-dark state approaches a ballistic detection limit as $\ell\to\infty$.

We establish a one-to-one correspondence between geodesics associated with the one-parameter family of $\alpha$-connections on the Gaussian statistical manifold and a class of continuous stochastic processes characterized by a time-independent noise intensity. We demonstrate that geodesics in expectation parameters naturally classify into three distinct geometric categories, among which the Boundary-connecting class allows us to construct an explicit linear stochastic realization with constant diffusion, representing a generalized bridge process. This result demonstrates how continuous stochastic processes within this Gaussian class can be extended along geometric curves. Under appropriate operational limits, this generalized bridge process reduces to fundamental stochastic dynamics, either Ornstein-Uhlenbeck (OU) relaxation or free Brownian diffusion. Crucially, the physical restoring force governing the resulting OU relaxation directly determines the underlying connection parameter $\alpha$, providing a concrete physical observable to constrain the manifold geometry. Depending on the chosen affine connection representation, this restoring force can be attributed either to scalar curvature or purely to non-metricity, establishing a direct conceptual analogy with the Geometrical Trinity of Gravity. Furthermore, applying this framework to driven stochastic thermodynamics, we show that the work-minimizing optimal protocol in the slow-driving limit coincides precisely with an expectation geodesic of the statistical manifold with non-metricity equipped with $(g, {}^{(1/2)}\Gamma, {}^{(-1/2)}\Gamma)$, highlighting the active physical role of non-metricity in information geometry.

Climate change poses a major scientific, environmental, and educational challenge, requiring approaches that connect physical concepts, empirical evidence, and socially relevant environmental issues. This study presents and analyzes a low-cost experimental investigation developed within the "Physics and the Environment" course of a Physics teacher training program at the State University of the Tocantina Region of Maranhão (UEMASUL), Brazil. The experiment involved constructing a simplified thermal simulator using accessible materials and comparing a confined system with an open control system, both exposed simultaneously to solar radiation. The results showed that the average temperature inside the simulator was $45.91^{\circ}\mathrm{C}$, compared to $38.58^{\circ}\mathrm{C}$ in the external control system, corresponding to a mean temperature difference of $7.33^{\circ}\mathrm{C}$ (among other analyses). These results demonstrate that the experimental setup was capable of producing and measuring a significant thermal difference between the two systems. However, the observed temperature rise should not be interpreted as a direct measure of the atmospheric greenhouse effect, given that the experimental apparatus involves both radiative and non-radiative heat transfer mechanisms. The study emphasizes the educational potential of low-cost experimentation as a strategy to integrate electromagnetic radiation, energy balance, temperature, heat transfer, and climate science into the initial training of physics teachers. It also highlights the importance of explicitly discussing the limitations of experimental models and distinguishing local experimental evidence from conclusions regarding global climate processes.

Nonreciprocity is increasingly recognized as a unifying concept linking diverse nonequilibrium phenomena found across physics, chemistry, and biology. It gives rise to distinctive behavior including run-and-chase dynamics and spatio-temporal patterns, often associated with a breaking of time-reversal symmetry. However, nonreciprocity and its nonequilibrium signatures are fundamentally scale-dependent, and may emerge or disappear under coarse-graining. A central challenge is therefore to understand when and how nonreciprocity manifests itself on different scales, for example via irreversible fluctuations or macroscopic currents. In this Perspective, we discuss the physical origin and fate of effective nonreciprocal interactions and the characteristic irreversible dynamics they give rise to across scales.

We numerically investigate how particle surface roughness affects the static and dynamic properties of a hard-particle fluid across a wide range of densities, rho. These simulations of a simple model of granular systems reveal that, although the amplitude and coverage of surface corrugation significantly influence the rho-dependence of system properties, the qualitative behavior of this dependence remains unchanged. These findings can be described quantitatively by introducing an effective particle size, which enables a direct mapping of the rough particle systems to equivalent hard-disk systems. Analytical calculations provide an explicit form of this mapping, and allow us to predict the static and dynamic properties of rough particles using standard liquid-state theories for hard disks.

This paper develops a generalization of Zubarev's nonequilibrium statistical operator method for the case of simultaneous inclusion of additive and nonlocal boundary functionals of trajectories. Using a unified thermodynamic approach, a three-parameter model of nonequilibrium systems is constructed, including the first-passage time, the dwell time above a given level, and the absolute extremum of the process. A correspondence is demonstrated between the maximum information entropy method for trajectories and the Donsker-Varadan large deviation formalism. Using the Doob`s h-transform, it is demonstrated that fixing extremal functionals of history induces efficient non-Markovian transport in the system with dynamic adaptation to historical records. Criteria for the applicability of the developed apparatus in the "large time" domain and the possibilities of its use for optimizing stochastic particle separation in periodic potentials are discussed.

We develop a least-action framework for describing how a probability distribution can evolve from an equilibrium state to a prescribed nonequilibrium state under constrained incremental changes. Taking a Gibbs distribution as the equilibrium reference, the framework gives a direct physical meaning to the geometry of the probability simplex: distance from equilibrium corresponds to nonequilibrium free energy, while changes between successive distributions carry an informational kinetic cost. The Pythagorean structure of relative entropy then provides the central insight of the work. It shows that intermediate distributions chosen via sequential information projections can reduce the kinetic cost of large transitions and establishes an energy-conservation-like relation between the kinetic expenditure along a path and the free energy accumulated in reaching the target distribution. Motivated by this geometry, we construct a greedy least-action path through successive information projections, obtain a closed-form characterization of each projection through the Lambert W function, and establish a finite-step performance guarantee. We further show that state-dependent costs can be incorporated naturally by reshaping the underlying Gibbs reference, providing a thermodynamic interpretation of path penalties as modifications of the effective energy landscape. Together, these results provide a unified view of distributional evolution through least action, information geometry, and nonequilibrium thermodynamics.

Neural networks acquire internal representations through learning. In this work, we formulate stochastic gradient descent (SGD) as a Markovian stochastic process and derive a Fisher-information flow speed limit that bounds the rate at which trainable parameters can acquire information about latent variables in the data-generating process. The resulting inequality decomposes the information flow into drift and noise contributions, thereby quantifying the roles of deterministic learning forces and SGD-induced fluctuations from an information-theoretic perspective. We verify the bound in analytically tractable basis-function linear regression, where the information budget predicted by the bound reproduces the ordering and characteristic time scales with which different latent variables are encoded in the learned parameters. These results establish Fisher-information speed limits as a quantitative framework for diagnosing when and how different aspects of the data-generating mechanism are acquired during stochastic learning.

We tabulate, on the diagonal, the $n$th power of the primitive approximation for the pair Coulomb density matrix on a sphere, with up to $n=5$, and we discuss its behavior at particles contact as $n$ grows. Our results show that even on a curved surface quantum statistical physics is fundamentally different from its classical counterpart. If in the latter one needs to artificially introduce a regularization of the divergent attractive Coulomb potential preventing particles contact, for example with a hard core, in the former this is not necessary.

An expository essay containing some new results. A learner holds a prior belief over Boolean maps that answer a finite set of $Q$ questions, and receives answers one by one. Each answer carries surprisal and can clear predictive uncertainty about both the question asked and questions still unasked. We quantify this effect by the leverage: table entropy cleared per bit of surprisal received. Taking expectations over the truth prior and the question order, define the aggregate leverage as the ratio of expected uncertainty cleared to expected surprisal received. It equals one for independent answers and can exceed one for correlated answers. At finite size, this ratio is determined exactly by a single sequence: the mean entropy $G_\ell$ of the answers to $\ell$ questions. As the number of input bits grows at fixed asked fraction $t=\ell/Q$, a limiting increment profile $\gamma(t)$ determines the macroscopic learning curve. With $\eta_0$ the limiting initial entropy per question, the leverage becomes $L(t)= \frac{\eta_0-(1-t)\gamma(t)} {\int_0^t\gamma(x),dx}$. For exchangeable priors, de Finetti's representation gives a constant bulk profile $\gamma(t)$: deduction is confined to a boundary layer at $t=0$, and the leverage is forced to a hyperbolic form, as surprisal grows linearly. By contrast, we construct a simplicity prior with nontrivial bulk learning by grading Boolean maps by their polynomial degree over $\mathbb{F}_2$ and allocating weight across degree classes through a CDF $F$. Reed-Muller capacity then yields $\gamma(t)=1-F(t)$. This realizes any nonincreasing profile taking values in $[0,1]$, together with the corresponding macroscopic leverage curve.

Stochastic models of gene expression typically begin with a microscopic model of transcription and propagate its statistics to the RNA distribution. Here we develop a doubly stochastic framework in which RNA production is Poisson conditional on a time-varying transcription rate $\lambda(t)$. For RNA lifetimes drawn independently from an arbitrary finite-mean distribution, we derive the RNA Fano factor in terms of the lifetime survival function and the autocovariance of $\lambda(t)$. For a Poisson degradation process with rate $\mu$, the survival kernel provides an exponential temporal filter, and the result depends only on the mean, variance, and normalized autocorrelation of $\lambda(t)$. These quantities may be calculated from an explicit rate model or, under ergodicity and adequate sampling, estimated from a sufficiently long rate trajectory. We validate the data-driven estimator using simulated transcription-rate trajectories, without supplying the known autocorrelation to the estimator. We also obtain exact analytical results for transcription-rate dynamics modeled by a discrete M/M/1 process and by drift-diffusion with reflecting, periodic, or first-passage-reset boundaries, and verify each result by direct simulation of the coupled transcription-rate and RNA copy-number processes.

The monomer-dimer model is one of the most well-known unsolved lattice models. In this paper we study the monomer-dimer model on the honeycomb lattice using the tensor network method, in the case that the dimer and monomer activities are 1. The monomer-dimer configurations are exactly mapped into the ground states of the antiferromagnetic Ising model on the Kagomé lattice in the critical field $H_{\rm{ex}}=4J$, and the tensor network is constructed based on the local ground states of each Ising triangle. The VUMPS approach is employed to contract the tensor network, providing a high-precision result of the monomer-dimer problem. We also revisit the edge coloring problem on the honeycomb lattice and discuss its relationship to the monomer-dimer model. Finally we formulate the monomer-dimer problem in the language of the sixteen-vertex model, and discuss the non-integrability of the general monomer-dimer model and the integrability of the pure dimer model.

We extend the recently proposed truncated Polyakov bootstrap to boundary conformal field theories (BCFTs). The formalism uses the analytic functional framework to find approximate solutions of BCFT crossing. We show that a generic nonperturbative solution can be identified by relating it to a family of deformations around generalized free fields (GFF) with a fixed boundary condition. We show this by tracking the flow of BCFT data from GFF with Neumann boundary condition to that with Dirichlet. The same method is then used for the 3d Ising special transition, using the perturbative Wilson-Fisher description as the deformation to identify it. The BCFT data obtained are in remarkable agreement with existing lattice results where available, and are otherwise new.

Characterizing the time evolution of generic quantum many-body systems is a fundamental challenge, as representing the exact state requires exponentially scaling computational resources. While hydrodynamics and statistical mechanics successfully simplify this task by predicting the expectation values of local observables, these macroscopic frameworks provide no information about nonlinear characteristics of the quantum state. In this work, we demonstrate that for systems exhibiting a timescale separation, with dynamics governed by the transport of conserved charges, this lost information can be systematically recovered. By constraining the maximum-entropy Scrooge ensemble solely by the system's slow modes, we accurately reconstruct complex, nonlinear quantum properties of the global time-evolved state, including the half-chain entanglement entropy and the participation entropy in the computational basis. Our results generalize the paradigm of canonical typicality, revealing that a hydrodynamically bottlenecked system behaves as a typical pure state within a dynamically restricted submanifold of the Hilbert space - a phenomenon we term global restricted typicality.

Recent developments have established exact bosonization and fermionization with a $\mathbb{Z}_2$ symmetry as dualities through gauging. In this work, we apply fermionic gauging, which realizes generalized Jordan-Wigner transformations, to the Bose-Hubbard (BH) model with a global $U(1)$ symmetry and derive an exact dual description in terms of fermionic composites, built from bosons and fermions. In 1D, this duality generalizes the exact mapping between the extended hard-core BH model and the spinless Fermi-Hubbard model to include soft-core bosons. At low energies, the mapping reduces to the well-known equivalence between the sine-Gordon model and the Thirring model. The oscillation wave vector of the fermionic composite correlation function in the gapless phase is fixed by their density, providing a novel manifestation of Luttinger's theorem. We verify the exact duality using density matrix renormalization group (DMRG) calculations and demonstrate that the gapless phase and the phase transition are governed by the compact boson conformal field theory. Our construction naturally extends to generic bosonic systems and higher dimensions, opening new avenues for studying Bose-Fermi mixtures in optical lattices and other strongly correlated quantum systems.

Cahn-Hilliard phase separation turns small composition fluctuations into coarsening domains. In Fourier space, the pattern forms a ring whose angular intensity favors an axis. We ask whether the axis favored early in an evolution remains related to the axis favored later in the same evolution. We analyze two-dimensional simulations with isotropic initial fluctuations and no imposed direction. We introduce $Q_2$, a normalized angular average over the Fourier spectrum, as a measure of the strength and direction of spectral anisotropy. Linear growth amplifies different wave numbers at different rates, selecting an early axis from the angular imbalances in the initial spectrum. This axis remains correlated with the late axis during coarsening. At a fixed time, shallow quenches show stronger early-late alignment. This advantage disappears when the quenches are compared at similar stages of domain growth. Adding the early $Q_2$ to a prediction based on quench depth, mean composition, and box size reduces the mean absolute error for late $Q_2$ by $3.53\%$. This reduction disappears when only the magnitude of the early $Q_2$ is retained, or when its direction is replaced by the direction from another evolution. The early Fourier intensity therefore carries information about the later state of the same evolving field.

We introduce the Terrain-Weighted Forest Fire Model (TFFM), a lattice model in which fire spreads on a spatially correlated Gaussian height field with the asymmetric bond probability $p_{i\to j}=\mathrm{clip}[e^{-\beta+\gamma(h_j-h_i)},0,1]$, plus an additive wind bias. Simulations on lattices up to $L=8192$ reveal a sharp active-to-inactive transition whose critical suppression threshold $\beta_c$ is even in $\gamma$, decreases with $|\gamma|$, and decreases as the terrain correlation length $\sigma_h$ is reduced: slope asymmetry acts as a suppressant because downhill bonds are penalized and fire stalls at local elevation maxima. For rough terrain and low tree density the fire fails to percolate even at zero suppression. Finite-size scaling on a fine $\beta$ grid at $L=2048$–$8192$ gives a correlation-length exponent $\nu=1.8\pm0.17$ from both the susceptibility peak and the width of the transition, and a front-velocity exponent $\delta=0.34\pm0.03$, identical for smooth and rough terrain; neither matches directed percolation ($\nu_\perp=0.73$, $\nu_\parallel-\nu_\perp\approx0.56$) or isotropic percolation ($\nu=4/3$, $\approx0.18$). The single-seed survival probability at $\beta_c$ is independent of $L$ and decays extremely slowly, with a running exponent falling from $\approx0.09$ to $\approx0.04$, excluding directed percolation and pointing to a survival probability that remains finite at criticality, consistent with the $L$-independent value $P^*\approx0.5$ at which $P_{\rm surv}$ drops to zero. Wind raises $\beta_c$ by a factor of $2$–$4$, produces a sharp onset of downwind fire-scar drift at weak coupling, and, at high terrain coupling, decreases the burned fraction at boundary crossing—a terrain-wind competition effect absent from isotropic bond-disorder models. The model yields fire-risk thresholds and fire-scar signatures comparable to satellite burn-scar data.

The concept of Markov chain Monte Carlo (MCMC) cycles, an analogy to cyclic processes in heat engines, is presented in order to examine Bayesian inference problems. In this effort, we develop adaptive ensemble schedulers that allow the tuning of external parameters of a Bayesian canonical ensemble during an MCMC run, realising the MCMC cycles in practice. We run these cycles on different statistical models. As a fundamental insight, we find (both theoretically and in practice) that such systems can produce a non-zero net work output if and only if the considered model is non-Gaussian. As such, they may serve as a measure of non-Gaussianity in Bayesian inference, which we test on an example from supernova cosmology.

The recently proposed Microcanonical Hamiltonian Monte Carlo algorithm has not yet been studied in detail from a thermodynamic point of view; this work aims to fill that gap. We demonstrate how thermodynamical state variables and potentials can be derived and thereby demonstrate that the construction of the algorithm formally represents a microcanonical thermodynamic ensemble. In particular, we demonstrate (analytically and numerically) that the algorithm fulfils the Helmholtz theorem, an alternative formulation of the first law of thermodynamics. Furthermore, we construct a new sampling algorithm that extends the original to lower-dimensional inference problems. Finally, we argue that canonical Markov Chain Monte Carlo algorithms are more natural than Microcanonical Hamiltonian Monte Carlo from the thermodynamic and information-theoretic point of view.