In classical physics, events follow a definite causal order: the past influences the future, but not the reverse. Quantum theory, however, permits superpositions of causal orders -- so-called indefinite causal orders -- which can provide operational advantages over classical scenarios. Verifying such phenomena has sparked significant interest, much like earlier efforts devoted to refuting local realism and confirming quantum entanglement. To date, demonstrations of indefinite causal order have all been based a process called the quantum switch and have relied on device-dependent or semi-device-independent protocols. Achieving a device-independent verification of indefinite causal order would imply that nature allows for correlations that do not respect causality, independent of any experimental assumptions or underlying theoretical description of the experiment. To this end, a recent theoretical development introduced a Bell-like inequality that allows for fully device-independent verification of indefinite causal order in a quantum switch. Here we implement this verification by experimentally violating this inequality. In particular, we measure a value of $1.8328 \pm 0.0045$, which is 18 standard deviations above the Definite Causal Order Bound of $1.75$. Our work presents the first implementation of a device-independent protocol to verify indefinite causal order, albeit in the presence of experimental loopholes. This represents an important step towards the device-independent verification of an indefinite causal order, and provides a context in which to identify loopholes specifically related to the verification of indefinite causal order.

An extended multiconfigurational dynamical symmetry (EMUSY) within the symplectic symmetry approach to clustering (SSAC) is proposed for the general case of multicluster nuclear systems. A characteristic property of the EMUSY is that it includes more general symplectic, i.e. number non-preserving, transformations which contain the standard number-preserving (unitary) multiconfigurational dynamical symmetry transformations as a special limiting case. In this way the EMUSY becomes able to connect various possible clusterizations of different multicluster type, as well as various many-particle configurations between the shell, collective and cluster models of nuclear structure. The theory is briefly illustrated using the nuclear system $^{24}$Mg as an example.

Understanding how the large-scale kinematics of the MW shape the formation and evolution of the interstellar medium remains challenging from an observational perspective, and numerical models that can reproduce the observed structure and kinematics of the MW are much needed in order to infer how the MW might work as a star formation engine. This work aims to use a numerical framework that is a close match to the observed large-scale distribution of stars and gas in the MW to isolate and understand the impact of galaxy-driven flows on the formation, agglomeration, and longevity of spiral patterns, prior to the inclusion of chemistry, star formation, and feedback. We use an isothermal simulation of a MW-like galaxy, found to closely match the longitude-velocity observational features of the MW in previous work, that includes the coupled evolution of gas, stars, and dark matter under purely gravitational and hydrodynamical processes. We characterise the morphology and kinematics of the stars and gas in the disc, quantify velocity residuals and their association with spiral features, and analyse the time-evolution of individual spiral-ridge segments. Our results demonstrate that our model reproduces many observed MW structural and kinematic signatures, from the inner Galaxy to the Solar neighbourhood, supporting its suitability as an analogue of the MW. The stellar spiral pattern in our model is relatively weak and shows lower multiplicity relative to the sharper gaseous arms, offering an explanation for discrepancies in observational determinations of the number and location of MW spiral arms. Both gas and stellar spiral arms are highly segmented, without a single coherent spiral pattern as expected from a grand-design type of galaxy. We find strong radial motions linked to the non-circular motions driven by the presence of a bar, and which extend well into the disc. The gas radial and...

We construct stochastic gradient flows on the $2$-Wasserstein space $\mathcal P_2$ over $\mathbb R^d$ for energy functionals of the type $W_F(ρd x)=\int_{\mathbb R^d}F(x,ρ(x))d x$. The functions $F$ and $\partial_2 F$ are assumed to be locally Lipschitz on $\mathbb R^d\times (0,\infty)$. This includes the relevant examples of $W_F$ as the entropy functional or more generally the Lyapunov function of generalized porous media equations. First we define a class of Gaussian-based measures $Λ$ on $\mathcal P_2$ together with a corresponding class of symmetric Markov processes ${(R_t)}_{t\geq 0}$. Next, using Dirichlet form techniques we perform stochastic quantization for the perturbations of these objects which result from multiplying such a measure $Λ$ by a density proportional to $e^{-W_F}$. Finally we show that the intrinsic gradient $DW_F(μ)$ is defined for $Λ$-a.e. $μ$ and that the Gaussian-based reference measure $Λ$ can be chosen in such way that the distorted process ${(μ_t)}_{t\geq 0}$ is a martingale solution for the equation $dμ_t=-DW_F(μ_t) d t+d R_t$, $t\geq 0$.

A typical Bayesian inference on the values of some parameters of interest $\bf q$ from some data $D$ involves running a Markov Chain (MC) to sample from the posterior $p({\bf q},{\bf n} | D) \propto \mathcal{L}(D | {\bf q},{\bf n}) p({\bf q}) p({\bf n}),$ where $\bf n$ are some nuisance parameters with separable prior. In some cases, the nuisance parameters are high-dimensional, and their prior $p({\bf n})$ is itself defined only by a set of samples that have been drawn from some other MC. The MC for the posterior will typically require evaluation of $p({\bf n})$ at arbitrary values of ${\bf n},$ i.e.\ one needs to provide a density estimator over the full $\bf n$ space from the provided samples. But the high dimensionality of $\bf n$ hinders both the density estimation and the efficiency of the MC for the posterior. We describe a solution to this problem: a linear compression of the $\bf n$ space into a much lower-dimensional space $\bf u$ which projects away directions in $\bf n$ space that cannot appreciably alter $\mathcal{L}.$ The algorithm for doing so is a slight modification to principal components analysis, and is less restrictive on $p(\bf n)$ than other proposed solutions to this issue. We demonstrate this ``mode projection'' technique using the analysis of 2-point correlation functions of weak lensing fields and galaxy density in the \textit{Dark Energy Survey}, where $\bf n$ is a binned representation of the redshift distribution $n(z)$ of the galaxies.

We study the sum of the squares of the irreducible character degrees not divisible by some prime $p$, and its relationship with the the corresponding quantity in a $p$-Sylow normalizer. This leads to study a recent conjecture by E. Giannelli, which we prove for $p=2$ and in some other cases.

Through the Hamilton-Jacobi equation of classical mechanics, BPS magnetized Baryonic layers (possessing both baryonic charge and magnetic flux) have been constructed in the gauged non-linear sigma model (G-NLSM) minimally coupled to Maxwell theory, which is one of the most relevant effective theories for Quantum Chromodynamics (QCD) in the strongly interacting low-energy limit which also takes into account the electromagnetic interactions. Since the topological charge that naturally appears on the right hand side of the BPS bound is a non-linear function of the baryonic charge, the thermodynamics of these magnetized Baryonic layers is highly non-trivial. In this work, using tools from the theory of Casimir effect, we derive analytical relationship between baryonic charge, topological charge, magnetic flux and relevant thermodynamical quantities (such as pressure, specific heat and magnetic susceptibility) of these layers. The critical Baryonic chemical potential is identified. Quite interestingly, the grand canonical partition function can be related with the Riemann zeta function. On the technical side, it is quite a remarkable result to derive explicit expressions for all these thermodynamics quantities of a strongly interacting magnetized system at finite Baryon density. The effects of the Isospin chemical potential can be included as well: in particular, we will be able to construct explicitly the BPS bound and the corresponding BPS configurations also in the case in which the Isospin chemical potential is non-zero. The physical interpretations of our analytical results will be discussed.

We investigate the impact of OH- ions incorporation on the lattice strain and spontaneous polarization of BaTiO3 nanorods synthesized under different conditions. It was confirmed that the lattice strain depends directly on Ba supersaturation, with higher supersaturation leading to an increase in the lattice strain. However, it was shown that crystal growth and observed lattice distortion are not primarily influenced by external strain; rather, OH- ions incorporation plays a key role in generating internal chemical strains and driving these processes. By using the less reactive TiO2 precursor instead of TiOCl2 and controlling Ba supersaturation, the slower nucleation rate enables more effective regulation of OH- ions incorporation and crystal growth. This in turn effects both particle size and lattice distortion, leading to c/a ratio of 1.013 - 1.014. The incorporation of OH- ions induces lattice elongation along the c-axis, contributing to anisotropic growth, increasing of the rod diameter and their growth-induced bending. However, the possibility of the curvature-induced changes in domain morphology of BaTiO3 nanorods remains almost unexplored. To study the possibility, we perform analytical calculations and finite element modeling, which provide insights into the curvature-induced changes in the strain-gradient, polarization distribution, and domain morphology in BaTiO3 nanorods. Theoretical results reveal the appearance of the domain stripes in BaTiO3 nanorod when the curvature exceeds a critical angle. The physical origin of the domain stripes emergence is the tendency to minimize its elastic energy of the nanorod by the domain splitting. These findings suggest that BaTiO3 nanorods, with curvature-controllable amount of domain stripes, could serve as flexible race-track memory elements for flexo-tronics and domain-wall electronics.

Biochemical reaction networks are widely applied across scientific disciplines to model complex dynamic systems. We investigate the diffusion approximation of reaction networks with mass-action kinetics, focusing on the identifiability of the stochastic differential equations associated to the reaction network. We derive conditions under which the law of the diffusion approximation is identifiable and provide theorems for verifying identifiability in practice. Notably, our results show that some reaction networks have non-identifiable reaction rates, even when the law of the corresponding stochastic process is completely known. Moreover, we show that reaction networks with distinct graphical structures can generate the same diffusion law under specific choices of reaction rates. Finally, we compare our framework with identifiability results in the deterministic ODE setting and the discrete continuous-time Markov chain models for reaction networks.

We propose and analyze two agent-based models to investigate the dynamics of papal conclaves, focusing on how social influence, strategic voting, and ideological alignment affect the time required to elect a pope. In the first model, cardinals interact through two mechanisms: with probability $p$, they imitate the choice of a randomly selected peer, and with probability $q$, they shift support to the most voted candidate from the previous round. Additionally, strategic behavior is introduced via ``useful voting'', where agents abandon their preferred candidate if he receives less than a threshold fraction of the votes, switching instead to the most viable alternative. A candidate must secure a qualified majority of two-thirds to be elected. We then extend the framework by incorporating ideological blocs, assigning each cardinal and candidate to one of two groups (e.g., progressives and conservatives). Cardinals initially vote for candidates from their own group but may cross ideological lines for strategic reasons. We initialize the electorate with $20\%$ conservative cardinals, reflecting the current composition shaped by papal appointments. Numerical simulations show that ideological polarization tends to delay the election by increasing the number of voting rounds required. However, higher values of strategic responsiveness $q$ can restore efficiency even under polarization. We further validate the model by calibrating parameters to historical data from conclaves held between 1939 and 2025. The model reproduces observed convergence times with good agreement, supporting its explanatory power across institutional contexts. The rapid outcome of the 2025 conclave, despite ideological divisions, suggests the importance of informal consensus-building, possibly prior to voting, as a key mechanism for accelerating convergence.

Let $X$ be a complex-projective variety with klt singularities and ample canonical divisor. We prove that $X$ is a quotient of the polydisc by a group acting properly discontinuously and freely in codimension one if and only if $X$ admits a semispecial tensor with reduced hypersurface. This extends a result of Catanese and Di Scala to singular spaces, and answers a question raised by these authors. As a key step in the proof, we establish the Bochner principle for holomorphic tensors on klt spaces in the negative Kähler--Einstein case.

In this article I study the variation of Selmer groups in families of modular Galois representations that are congruent modulo a fixed prime $p \geq 5$. Motivated by analogies with Goldfeld's conjecture on ranks in quadratic twist families of elliptic curves, I investigate the stability of Selmer groups defined over $\mathbb{Q}$ via Greenberg's local conditions under congruences of residual Galois representations. Let $X$ be a positive real number. Fix a residual representation $\barρ$ and a corresponding modular form $f$ of weight $2$ and optimal level. I count the number of level-raising modular forms $g$ of weight $2$ that are congruent to $f$ modulo $p$, with level $N_g\leq X$, such that the $p$-rank of the Selmer groups of $g$ equals that of $f$. Under some mild assumptions on $\barρ$, I prove that this count grows at least as fast as $X (\log X)^{α- 1}$ as $X \to \infty$, for an explicit constant $α> 0$. The main result is a partial generalization of theorems of Ono and Skinner on rank-zero quadratic twists to the setting of modular forms and Selmer groups.

We calculate the magnon dispersion spectra of the two-dimensional zigzag van der Waals antiferromagnet NiPS$_3$ for monolayer, bilayer, and bulk systems as a function of an external magnetic field. We calculate the exchange and anisotropy constants in our spin model by first principles. We can accurately explain the transition from a collinear to a canted ground state for a magnetic field applied normal to the (in-plane) easy-axis, and a spin-flop transition when the field is parallel to it. A topologically protected Dirac nodal line is present and robust with respect to both external and anisotropy fields.

Let $L$ be a link in $S^3$. We consider the class of meridional presentations for $π_1(S^3\backslash L)$ in which the relations are witnessed by embedded two-spheres which can be represented simultaneously in a fixed diagram of $L$, analogously to decomposition spheres studied by Cromwell, Menasco and others. Wirtinger relations are witnessed by such spheres and the Wirtinger presentation is a special case of the ones we study. We prove that the smallest number of generators of $π_1(S^3\backslash L)$ over all such presentations equals the bridge number of $L$.

The recursion method, which solves coupled Heisenberg equations in a Lanczos operator basis, has recently emerged as a powerful nonperturbative tool for computing dynamical correlation functions in strongly correlated two- and three-dimensional quantum many-body systems. Motivated by this success, we investigate whether the method can be extended to expectation values of observables following a quantum quench. We find that such an extension encounters an obstacle absent in the computation of dynamical correlation functions. The latter are fully determined by the Lanczos coefficients $b_n$, which in generic systems exhibit universal behavior, enabling reliable extrapolation from the first few dozens of explicitly computed coefficients. In contrast, quench dynamics additionally requires "quench coefficients" $c_n$, defined as overlaps of Lanczos basis operators with the initial state. We show that, unlike the Lanczos coefficients, the quench coefficients display no universal structure and cannot be reliably extrapolated, thereby limiting the time up to which the method yields accurate results. The behavior of quench coefficients is highly state-dependent, ranging from decaying to irregular or even growing sequences; typically, the less regular the sequence $c_n$, the shorter the accessible timescale. Nevertheless, for favorable initial states, the method remains competitive with state-of-the-art approaches.

Qualifying new detectors in test beam environments presents a challenging setting that requires stable operation of diverse devices, often employing multiple data acquisition systems. Changes to these setups are frequent, such as using different reference detectors depending on the facility. Managing this complexity necessitates a system capable of controlling the data taking, monitoring the experimental setup, facilitating seamless configuration, and easy integration of new devices. One aspect of such systems is network configuration. Many systems require fixed IP addresses for all machines participating in the data acquisition, which adds complexity for users. In this paper, a network protocol for network discovery tailored towards network-distributed control and data acquisition systems is described.

Metallic coatings are used to enhance the durability of metal surfaces by protecting them from corrosion. These protective layers are typically deposited in a fluid state via a liquid film. Controlling instabilities in the liquid film is crucial to achieving uniform, high-quality coatings. This study explores the possibility of controlling liquid films on a moving substrate using a combination of gas jets and electromagnetic actuators. To model the 3D liquid film, we extend existing integral models to incorporate the effects of electromagnetic actuators. The control strategy was developed within a reinforcement learning framework, in which the Proximal Policy Optimisation (PPO) algorithm interacts with the liquid film via pneumatic and electromagnetic actuators to optimise a reward function that accounts for instability-wave amplitude through a trial-and-error process. The PPO identified an optimal control law that reduced interface instabilities via a novel mechanism: gas jets push crests, and electromagnets raise troughs via the Lorentz force.

We explain the linear algebraic framework provided by Tate modules of isogenous abelian varieties in a category-theoretic way.

Recent work by Google DeepMind introduced assembly-optimized sorting networks that achieve faster performance for small fixed-size arrays (3-8). In this research, we investigate the integration of these networks as base cases in classical divide-and-conquer sorting algorithms, specifically Merge Sort and Quick Sort, to leverage these efficient sorting networks for small subarrays generated during the recursive process. We conducted benchmarks with 11 different optimization configurations and compared them to classical Merge Sort and Quick Sort. We tested the configurations with random, sorted and nearly sorted arrays. Our optimized Merge Sort, using a configuration of three sorting networks (sizes 6, 7, and 8), achieves at least 1.5x speedup for random and nearly sorted arrays, and at least 2x speedup for sorted arrays, in comparison to classical Merge Sort. This optimized Merge Sort surpasses both classical Quick Sort and similarly optimized Quick Sort variants when sorting random arrays of size 10,000 and larger. When comparing our optimized Quick Sort to classical Quick Sort, we observe a 1.5x speedup using the 3-to-5 configuration on sorted arrays of size 10,000. The 6-to-8 configuration maintains a consistent 1.5x improvement across sorted arrays from 25,000 to 1 million elements. Our findings demonstrate the potential of integrating AI-optimized sorting networks to enhance the performance of classical sorting algorithms.

Holonomic quantum computation exploits the geometric evolution of eigenspaces of a degenerate Hamiltonian to implement unitary evolution of computational states. In this work we introduce a framework for performing scalable quantum computation in atom experiments through a universal set of fully holonomic adiabatic gates. Through a detailed differential geometric analysis, we elucidate the geometric nature of these gates and their inherent robustness against classical control errors and other noise sources. The concepts that we introduce here are expected to be widely applicable to the understanding and design of error robustness in generic holonomic protocols. To underscore the practical feasibility of our approach, we contextualize our gate design within recent advancements in Rydberg-based quantum computing and simulation.

In this paper we study an $L^{2k}$-analogue of Bohr's abscissae of summability for polynomially bounded analytic functions in a strip. An approximate concavity in $k$ is shown to be equivalent to convexity of the reciprocal of the order function. For $L$-functions in the extended Selberg class, this implies that the order function is everywhere differentiable and has quadratic decay near one. We also establish a connection between strict concavity and the Lindelöf hypothesis.

Graph neural networks (GNNs) have proven to be an effective tool for enhancing the performance of recommender systems. However, these systems often suffer from popularity bias, leading to an unfair advantage for frequently interacted items, while overlooking high-quality but less popular items. In this paper, we propose a GNN-based recommendation model that disentangles popularity and quality to address this issue. Unlike existing methods that treat all long-tail items uniformly, our approach introduces an edge classification technique to differentiate between popularity bias and genuine quality disparities among items. Furthermore, it uses cost-sensitive learning to adjust the misclassification penalties, ensuring that underrepresented yet relevant items are not unfairly disregarded. Experimental results demonstrate improvements in fairness metrics by approximately $32\%$ on average across different scenarios while maintaining competitive accuracy, with only minor variations compared to state-of-the-art methods.

In this paper, we prove two theorems concerning the test properties of the Frobenius endomorphism over commutative Noetherian local rings of prime characteristic $p$. Our first theorem generalizes a result of Funk-Marley on the vanishing of Ext and Tor modules, while our second theorem generalizes one of our previous results on maximal Cohen-Macaulay tensor products. In these earlier results, we replace $^{e}R$ with a more general module $^{e}M$, where $R$ is a Cohen-Macaulay ring, $M$ is a Cohen-Macaulay $R$-module with full support, and $^{e}M$ is the module viewed as an $R$-module via the $e$-th iteration of the Frobenius endomorphism. We also provide examples and present applications of our results, yielding new characterizations of the regularity of local rings.

The Hubble constant ($H_0$) is essential for understanding the universe's evolution. Different methods, such as Affine Invariant Markov chain Monte Carlo Ensemble sampler (EMCEE), Gaussian Process (GP), and Masked Autoregressive Flow (MAF), are used to constrain $H_0$ using $H(z)$ data. However, these methods produce varying $H_0$ values when applied to the same dataset. To investigate these differences, we compare the methods based on their sensitivity to individual data points and their performance in constraining $H_0$. We apply Monte Carlo delete-$d$ jackknife (MCDJ) to assess their sensitivity to individual data points. Our findings reveal that GP is more sensitive to individual data points than both MAF and EMCEE, with MAF being more sensitive than EMCEE. Sensitivity also depends on redshift: EMCEE and GP are more sensitive to $H(z)$ at higher redshifts, while MAF is more sensitive at lower redshifts. In simulation-based performance tests, we generate an ensemble of mock CC datasets with a fixed input truth $H_{0,\mathrm{true}}$, apply each method to recover $H_0$ posteriors, and summarise performance by comparing the recovered posterior to $H_{0,\mathrm{true}}$: (i) posterior central value accuracy (bias and RMSE), (ii) credible-interval calibration (68\% and 95\% coverage), and (iii) overall posterior quality (log score), under two simulation prescriptions ($Λ$CDM-based and GP-based). Overall, EMCEE performs best, GP is intermediate, and MAF performs worst across the performance metrics.

The studies of Bonaventura Cavalieri's indivisibles by Giusti, Andersen, Mancosu and others provide a comprehensive picture of Cavalieri's mathematics, as well as of the mathematical objections to it as formulated by Paul Guldin and other critics. An issue that has been studied in less detail concerns the theological underpinnings of the contemporary debate over indivisibles, its historical roots, the geopolitical situation at the time, and its relation to the ultimate suppression of Cavalieri's religious order. We analyze sources from the 17th through 21st centuries to investigate such a relation.

This study demonstrates that two-dimensional talc, a naturally abundant mineral, supports hyperbolic phonon-polaritons (HPhPs) at mid-infrared wavelengths, thus offering a low-cost alternative to synthetic polaritonic materials. Using scattering scanning near-field optical microscopy (s-SNOM) and synchrotron infrared nano spectroscopy (SINS), we reveal tunable HPhP modes in talc flakes of a long lifetime. These results highlight the potential of natural 2D talc crystals to constituting an effective platform for establishing scalable optoelectronic and photonic devices.

Sizing a residential microgrid efficiently requires solving a coupled design-and-operation problem: photovoltaic (PV) and battery capacities should be chosen in a way that reflects how the system will actually be dispatched over time. This paper proposes BOOST, or Battery-solar Ordinal Optimization Sizing Technique, which combines ordinal optimization (OO) with mixed-integer linear programming (MILP). OO is used to screen a large set of candidate battery/PV designs with a simple linear model and then re-evaluate only the most promising designs with a more accurate MILP that captures diesel commitment logic. Relative to the original short paper, this expanded manuscript retains the full methodological narrative but refreshes the quantitative section using a new synthetic benchmark dataset suite generated from the released clean reimplementation. The suite contains five yearly synthetic datasets/configurations: base, cheap battery, cheap PV, expensive diesel, and high peak tariff. On the base synthetic dataset, the best accurate design is a 500 kWh battery with 1833.3 kW of PV, achieving 13.169 c/kWh, while BOOST improves upon dynamic programming and greedy baselines. Across the full 10 x 10 design grid, the LP and MILP rankings are effectively identical (rho = 1.000), the paper-style choice of N = 90 and s = 18 recovers the global accurate optimum, and the OO-based workflow reduces runtime by 51.8% relative to exhaustive accurate evaluation on the refreshed synthetic benchmark run. Because these added datasets are synthetic, they should be read as methodological stress tests rather than as direct empirical claims about any specific real-world site. Code is available at https://github.com/MFHChehade/Microgrid-Optimization.

Let $S$ be a complex smooth projective surface with a genus two fibration, and $\mathrm{Aut}_s(S)$ the group of symplectic automorphisms, fixing every holomorphic 2-forms (if any) on $S$. Based on the work of Jin-Xing Cai, we observe in this paper that, if $χ(\mathcal{O}_S)\geq 5$, then $|\mathrm{Aut}_s(S)|\leq 2$. Then we go on to verify, under some conditions, that $\mathrm{Aut}_s(S)$ acts trivially on the Albanese kernel $\mathrm{CH}_0(S)_{\mathrm{alb}}$ of the 0-th Chow group, which is predicted by a conjecture of Bloch and Beilinson. As a consequence, if an automorphism $σ\in \mathrm{Aut}(S)$ acts trivially on $H^{i,0}(S)$ for $0\leq i\leq 2$, then it also acts trivially on $\mathrm{CH}_0(S)_{\mathrm{alb}}$.

In 2017, Nikiforov introduced the concept of the $A_α$-matrix, as a linear convex combination of the adjacency matrix and the degree diagonal matrix of a graph. This matrix has attracted increasing attention in recent years, as it serves as a unifying structure that combines the adjacency matrix and the signless Laplacian matrix. In this paper, we present some bounds for the largest and smallest eigenvalue of $A_α$-matrix involving invariants associated to graphs.

This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the partition function of the relevant physical quantities over a spacetime parametrized by coordinates. The partition yields a probabilistic interpretation that, based on Feynman's path integral formulation, leads to a dynamical law that generalizes the Schrödinger equation. A variety of systems can be put into the form proposed here, including particles in potentials, as well as matter and interaction fields. The main advantage of the proposed framework is that it presents the space of properties separately from that of the space of coordinates, whereas the dynamical law can be interpreted as the equation of two differential structures, one from each of these spaces. The resulting framework shows possibilities to further study physical quantities that relate directly to the spacetime coordinates, whose dynamics is best described in thermodynamical, rather than Hamiltonian, terms. A notable example is the theory of general relativity, in which the case of a scalar field in a Robertson-Walker metric is explored.