arXiv subjects

Michal Pavelka

Publications and source records attributed to Michal Pavelka.

At least 19 recordsLinked to original sources

arXiv2026

Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentials

We introduce Nonlinear GENERIC-Embedded Neural Networks (N-GENNs), a deep learning framework for discovering evolution equations of systems governed by the nonlinear GENERIC formalism (General Equation for Non-Equilibrium Reversible-Irreversible Coupling). Such systems exhibit coupled conservative and dissipative dynamics, and can be described via the superposition of a Hamiltonian flow and a generalized gradient flow. In contrast to existing approaches, our formulation incorporates generalized gradient flows via convex dissipation potentials, enabling the identification of a broader class of thermodynamically consistent dynamics, including systems with non-quadratic dissipation potentials. Thermodynamic structure is strongly enforced by construction through suitable reparameterizations of both the reversible operator and the dissipation potential, ensuring exact compliance with the first and second laws of thermodynamics. We validate the proposed approach on three representative examples: a harmonic oscillator coupled to a heat bath, an idealized chemical motor, and a one-dimensional viscoplastic model of Perzyna type. These results demonstrate the method's ability to accurately infer thermodynamically consistent models from data for systems incorporating both conservative and nonlinear dissipative dynamics.

physics.comp-ph↗

arXiv2026

How the arrow of time emerges from Hamiltonian systems by our incomplete knowledge

How does the arrow of time (dissipative, irreversible behavior) emerge from time-reversible Hamiltonian mechanics? Two ingredients are needed: the underlying system must be ergodic or phase-mixing, and our knowledge of the system must be incomplete. When the detailed dynamics explores its phase space and stays close to a submanifold parametrized by a reduced set of state variables, the lack-of-fit reduction method reveals that the effective equations for those reduced variables are necessarily irreversible. To make this precise, we present a path-integral formulation of the lack-of-fit reduction in non-equilibrium thermodynamics, which shows how the GENERIC framework (reversible Hamiltonian part plus irreversible gradient flow) emerges from purely Hamiltonian mechanics without any fitting parameters. The formulation is based on the Onsager-Machlup variational principle, and it yields reduced dynamical equations by minimizing the information discrepancy between the detailed and reduced evolutions. Subsequently, the reduction method is illustrated on the Kac--Zwanzig model, confirming that dissipation emerges from ignoring degrees of freedom, and on diffusion, where diffusion equation for the hydrodynamic mass density emerges from Vlasov equation. We also show how to generalize the Fisher information matrix and Kullback--Leibler divergence to arbitrary concave entropies via the principle of maximum entropy, including non-Boltzmann-Gibbs cases such as the Tsallis--Havrda--Charvát entropy.

cond-mat.stat-mech↗

arXiv2026

Contact Geometry of Relativistic Particle Motion

We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space consisting of four position coordinates, four momenta, and an additional variable (functioning as a geometric variant of the particle's proper time). In this setting, the evolution is generated by an evolution contact vector field with a contact Hamiltonian encoding the mass shell. By promoting the proper time to an independent variable, the relativistic Hamilton canonical equations are rewritten in a fully geometric form without having to identify the proper time with a parameter along the worldlines. This makes for instance the evolution of massless particles (photons) well-defined without the need of reparametrization. The framework is then applied to decaying particles. Finally, we formulate a covariant kinetic theory and show how decaying particles can be described geometrically in this framework, changing the entropy.

math-ph↗

arXiv2026

Comparison of some geometric frameworks for dissipative evolution in multiscale non-equilibrium thermodynamics

In this paper, we review and compare some geometric frameworks for dissipation in non-equilibrium thermodynamics. We start with a brief overview of classical irreversible thermodynamics and gradient dynamics. Then we discuss several specific frameworks including Rayleigh dissipation potential and the dissipative d'Alembert framework, showing their relations with gradient dynamics. Finally, we discuss frameworks for dissipative evolution generated from Poisson brackets.

cond-mat.stat-mech↗

arXiv2025

Assignment-Routing Optimization: Solvers for Problems Under Constraints

We study the Joint Routing-Assignment (JRA) problem in which items must be assigned one-to-one to placeholders while simultaneously determining a Hamiltonian cycle visiting all nodes exactly once. Extending previous exact MIP solvers with Gurobi and cutting-plane subtour elimination, we develop a solver tailored for practical packaging-planning scenarios with richer constraints.These include multiple placeholder options, time-frame restrictions, and multi-class item packaging. Experiments on 46 mobile manipulation datasets demonstrate that the proposed MIP approach achieves global optima with stable and low computation times, significantly outperforming the shaking-based exact solver by up to an orders of magnitude. Compared to greedy baselines, the MIP solutions achieve consistent optimal distances with an average deviation of 14% for simple heuristics, confirming both efficiency and solution quality. The results highlight the practical applicability of MIP-based JRA optimization for robotic packaging, motion planning, and complex logistics .

cs.AI↗

arXiv2025

Assignment-Routing Optimization : Efficient Heuristic Solver with Shaking Algorithm

This paper works on heuristic solver for joint assignment and routing optimization problem. Study on previous works shows that MIP based exact solvers can only provide efficient solutions for small to moderate size problems, due to exponentially growing computational complexity. This paper proposes to start with high quality initial guess through Hungarian algorithm based assignment and heuristic cycle merging algorithm. Subsequently, the solution is improved based on a proposed shaking algorithm to improve the assignment and routing sequence. In addition, the shaking approach also enables the Simulated Annealing algorithm to further improve the solution, which is very difficult if it is purely based on random sampling updates of item and placeholder sequences. Extensive experimental validation comparing with ground truth from the previously shared database shows that the introduced solver is much more efficient than the Gurobi solver especially for large size problems, with a 1000 node pair problem being solved within 1 min in Python implementation. The solution accuracy is within a percent in general as compared with ground truth in database. Although there are spaces for the proposed solver to be further improved with better accuracy, it works for practical applications with acceptable path quality and sufficient solver efficiency. Such shaking algorithms based solvers can also be applied to more general joint assignment and routing optimization problem with multiple type of items and corresponding placeholders. GitHub repository: https://github.com/QL-YUAN/Joint-Assignment-Routing-Optimization-Heuristic.git

math.CO↗

arXiv2025

On Geometry of Dissipation in Multiscale Dynamics and Thermodynamics

This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the phase-space volume itself becomes an additional dynamical variable. Second, we develop a new and simpler geometric formulation of the GENERIC framework, unifying Hamiltonian and gradient dynamics in a contact-geometric setting. This is realized within a specifically constructed graph space, which naturally emerges as an intermediate structure in the geometric Hamilton-Jacobi framework. Finally, we formulate a geometric extension of non-equilibrium thermodynamics in the setting of geometric Hamilton-Jacobi theory, allowing for the inclusion of microturbulence - a key feature of complex dynamical systems.

math-ph↗

arXiv2025

Classical and Multiscale Non-equilibrium Thermodynamics

Classical and multiscale non-equilibrium thermodynamics have different histories and different objectives. In this Note we explain the differences and review some topics in which the multiscale viewpoint of mesoscopic time evolution of macroscopic systems helped to advance the classical non-equilibrium thermodynamics. Eventually, we illustrate the Braun-Le Chatelier principle in dissipative thermodynamics.

cond-mat.stat-mech↗

arXiv2025

A geometric one-fluid model of superfluid helium-4

A standard description of superfluid helium-4 is based on the concept of two components (superfluid and normal), which leads to the so called two-fluid models. However, as there are no two kinds of atoms in helium-4, the two components can not be separated. Superfluid helium-4 is not a mixture of two components, being rather a single fluid with two motions. Here, we present a geometric one-fluid model of superfluid helium-4, which is based on the Hamiltonian formulation of fluid mechanics. The model is derived from the kinetic theory of excitations (treated as an ideal Bose gas under the temperature $1.3K$) and average particle motions. It can be simplified to the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) two-fluid model, where it removes one fitting parameter from the HVBK model, but it also gives extra terms beyond the HVBK model. Actually, we show that the two-fluid models are problematic in case of higher counter-flow velocities, where the usual splitting of total momentum to the superfluid and normal component becomes impossible. Finally, we show how vortex line density may be added to the state variables. The one-fluid model can be seen as a generalization of the two-fluid models that is geometrically consistent, fully compressible, with non-zero superfluid vorticity, and compatible with classical experiments.

cond-mat.supr-con↗

arXiv2025

Action-Minimization Meets Generative Modeling: Efficient Transition Path Sampling with the Onsager-Machlup Functional

Transition path sampling (TPS), which involves finding probable paths connecting two points on an energy landscape, remains a challenge due to the complexity of real-world atomistic systems. Current machine learning approaches use expensive, task-specific, and data-free training procedures, limiting their ability to benefit from high-quality datasets and large-scale pre-trained models. In this work, we address TPS by interpreting candidate paths as trajectories sampled from stochastic dynamics induced by the learned score function of pre-trained generative models, specifically denoising diffusion and flow matching. Under these dynamics, finding high-likelihood transition paths becomes equivalent to minimizing the Onsager-Machlup (OM) action functional. This enables us to repurpose pre-trained generative models for TPS in a zero-shot manner, in contrast with bespoke, task-specific approaches in previous work. We demonstrate our approach on varied molecular systems, obtaining diverse, physically realistic transition pathways and generalizing beyond the pre-trained model's original training dataset. Our method can be easily incorporated into new generative models, making it practically relevant as models continue to scale and improve with increased data availability. Code is available at github.com/ASK-Berkeley/OM-TPS.

cs.LG↗

arXiv2025

Internal tensorial variables and a heat transport equation with inertial, thermal viscosity and vorticity terms

Phonon hydrodynamics describes the motions of heat carriers (phonons) at sub-continuum scales: diffusive, ballistic, viscous, and vortical. In a previous paper, these behaviours were investigated within the framework of non-equilibrium thermodynamics with internal variables at the macroscopic scale, deriving generalizations of the Guyer-Krumhansl equation. In particular, a generalized heat conduction equation, containing not only the Fourier, Maxwell-Vernotte-Cattaneo, and Guyer-Krumhansl contributions, but also a term describing phonon vortices, was obtained. In this paper, we provide new insight and clarifications into the same model for rigid heat-conducting media. Then, we a posteriori identify two non-local macroscopic internal variables, $Q^s$ and $Q^a$ (the symmetric part and the antisymmetric part of a second order tensor $Q$) with the symmetric (changed in sign) and antisymmetric gradients of the heat flux, $-(\nabla J(q))^s$ and $(\nabla J(q))^{a}$. Also an identification of these two tensorial internal variables is obtained by an asymptotic approach. This generalizes the heat equation with additional terms containing the time derivative of the heat flux describing the viscous and vortical motions of phonons. These terms may describe the transfer from ordered rotational motion of phonon vortices to rotational microscopic motions of diatomic particles constituting complex polar crystals, in analogy to the hydrodynamics of classical micropolar fluids. Therefore, this paper fits into the currently explored area of phonon vorticity and its interactions with the heat flux itself.

cond-mat.mes-hall↗

arXiv2024

Conformal and Contact Kinetic Dynamics and Their Geometrization

We propose a conformal generalization of the reversible Vlasov equation of kinetic plasma dynamics, called conformal kinetic theory. In order to arrive at this formalism, we start with the conformal Hamiltonian dynamics of particles and lift it to the dynamical formulation of the associated kinetic theory. The resulting theory represents a simple example of a geometric pathway from dissipative particle motion to dissipative kinetic motion. We also derive the kinetic equations of a continuum of particles governed by the contact Hamiltonian dynamics, which may be interpreted in the context of relativistic mechanics. Once again we start with the contact Hamiltonian dynamics and lift it to a kinetic theory, called contact kinetic dynamics. Finally, we project the contact kinetic theory to conformal kinetic theory so that they form a geometric hierarchy.

math-ph↗

arXiv2024

Approaches to conservative Smoothed Particle Hydrodynamics with entropy

Smoothed particle hydrodynamics (SPH) is typically used for barotropic fluids, where the pressure depends only on the local mass density. Here, we show how to incorporate the entropy into the SPH, so that the pressure can also depend on the temperature, while keeping the growth of the total entropy, conservation of the total energy, and symplecticity of the reversible part of the SPH equations. The SPH system of ordinary differential equations with entropy is derived by means of the Poisson reduction and the Lagrange-Euler transformation. We present several approaches towards SPH with entropy, which are then illustrated on systems with discontinuities, on adiabatic and nonadiabatic expansion, and on the Rayleigh-Beenard convection without the Boussinesq approximation. Finally, we show how to model hyperbolic heat conduction within the SPH, extending the SPH variables with not only entropy but also a heat-flux-related vector field.

physics.flu-dyn↗

arXiv2023

Nonequilibrium model for compressible two-phase two-pressure flows with surface tension

In continuum thermodynamics, models of two-phase mixtures typically obey the condition of pressure equilibrium across interfaces between the phases. We propose a new non-equilibrium model beyond that condition, allowing for microinertia of the interfaces, surface tension, and different phase pressures. The model is formulated within the framework of Symmetric Hyperbolic Thermodynamically Compatible equations, and it possesses variational and Hamiltonian structures. Finally, via formal asymptotic analysis, we show how the pressure equilibrium is restored when fast degrees of freedom relax to their equilibrium values.

physics.flu-dyn↗

arXiv2023

Direct Poisson neural networks: Learning non-symplectic mechanical systems

In this paper, we present neural networks learning mechanical systems that are both symplectic (for instance particle mechanics) and non-symplectic (for instance rotating rigid body). Mechanical systems have Hamiltonian evolution, which consists of two building blocks: a Poisson bracket and an energy functional. We feed a set of snapshots of a Hamiltonian system to our neural network models which then find both the two building blocks. In particular, the models distinguish between symplectic systems (with non-degenerate Poisson brackets) and non-symplectic systems (degenerate brackets). In contrast with earlier works, our approach does not assume any further a priori information about the dynamics except its Hamiltonianity, and it returns Poisson brackets that satisfy Jacobi identity. Finally, the models indicate whether a system of equations is Hamiltonian or not.

math-ph↗

arXiv2022

Multiscale heat transport with inertia and thermal vortices

In this paper, we present a Hamiltonian and thermodynamic theory of heat transport on various levels of description. Transport of heat is formulated within kinetic theory of polarized phonons, kinetic theory of unpolarized phonons, hydrodynamics of polarized phonons, and hydrodynamics of unpolarized phonons. These various levels of description are linked by Poisson reductions, where no linearizations are made. Consequently, we obtain a new phonon hydrodynamics that contains convective terms dependent on vorticity of the heat flux, which are missing in the standard theories of phonon hydrodynamics. Moreover, the equations are hyperbolic and Galilean invariant, unlike current theories for beyond-Fourier heat transport. The vorticity-dependent terms violate the alignment of the heat flux with the temperature gradient even in the stationary state, which is expressed by a Fourier-Crocco equation. The new terms also cause that temperature plays in heat transport a similar role as pressure in aerodynamics.

cond-mat.mes-hall↗

arXiv2022

Unified description of fluids and solids in Smoothed Particle Hydrodynamics

Smoothed Particle Hydrodynamics (SPH) methods are advantageous in simulations of fluids in domains with free boundary. Special SPH methods have also been developed to simulate solids. However, there are situations where the matter behaves partly as a fluid and partly as a solid, for instance, the solidification front in 3D printing, or any system involving both fluid and solid phases. We develop an SPH-like method that is suitable for both fluids and solids at the same time. Instead of the typical discretization of hydrodynamics, we discretize the Symmetric Hyperbolic Thermodynamically Compatible equations (SHTC), which describe both fluids, elastic solids, and visco-elasto-plastic solids within a single framework. The resulting SHTC-SPH method is then tested on various benchmarks from the hydrodynamics and dynamics of solids and shows remarkable agreement with the data.

physics.flu-dyn↗

arXiv2022

A multiscale thermodynamic generalization of Maxwell-Stefan diffusion equations and of the dusty gas model

Despite the fact that the theory of mixtures has been part of non-equilibrium thermodynamics and engineering for a long time, it is far from complete. While it is well formulated and tested in the case of mechanical equilibrium (where only diffusion-like processes take place), the question how to properly describe homogeneous mixtures that flow with multiple independent velocities that still possess some inertia (before mechanical equilibrium is reached) is still open. Moreover, the mixtures can have several temperatures before they relax to a common value. In this paper, we derive a theory of mixtures from Hamiltonian mechanics in interaction with electromagnetic fields. The resulting evolution equations are then reduced to the case with only one momentum (classical irreversible thermodynamics), providing a generalization of the Maxwell-Stefan diffusion equations. In a next step, we reduce that description to the mechanical equilibrium (no momentum) and derive a non-isothermal variant of the dusty gas model. These reduced equations are solved numerically, and we illustrate the results on efficiency analysis, showing where in a concentration cell efficiency is lost. Finally, the theory of mixtures identifies the temperature difference between constituents as a possible new source of the Soret coefficient. For the sake of clarity, we restrict the presentation to the case of binary mixtures; the generalization is straightforward.

cond-mat.stat-mech↗