PhysDrive: Physics-Driven Control & Dataset

• PhysDrive is a physics-driven framework that embeds drive variables directly into system dynamics to regulate nonequilibrium transport, relaxation, memory, and sensing.
• It supports diverse applications from granular fluids and quantum many-body systems to model-based reinforcement learning and mechanical control in hybrid vehicles.
• PhysDrive also names a comprehensive in-vehicle multimodal dataset, capturing RGB, NIR, and mmWave data for robust physiological driver monitoring in real-world conditions.

PhysDrive refers to a family of physics-driven strategies in which a deliberately chosen drive variable is used to regulate transport, relaxation, memory, or sensing, and it also names a recent multimodal dataset for in-vehicle physiological monitoring. In the cited literature, the driving variable may be a bulk stochastic kick in a granular fluid, a body force on oppositely driven disks, an oscillating linear potential in a disordered quantum chain, strain in a spin-mechanical device, a global angular-velocity cycle for bistable material bits, or an energy-routed latent transition in a world model. Taken together, these works suggest that PhysDrive is best understood not as a single formalism but as a recurring design principle: embed the drive directly into the governing dynamics, power balance, or control objective so that nonequilibrium structure becomes a controllable resource rather than a disturbance (Kranz et al., 2010, Reichhardt et al., 2017, Bairey et al., 2017, Barfuss et al., 2015, Luan et al., 18 May 2026, Wang et al., 25 Jul 2025).

1. Conceptual scope

A unifying feature of PhysDrive is that the drive appears explicitly in the evolution law. In the oppositely driven disk system, the overdamped dynamics are

$$\eta \frac{d\mathbf{R}_i}{dt}=\sum_{j\neq i}\mathbf{F}_{ij}^{\rm int}+\mathbf{F}_i^{\rm drive},$$

with species-dependent body forces along $\pm x$; in PH-Dreamer, the canonical Port-Hamiltonian template is

$\dot{x}=[J(x)-R(x)]\,\nabla_x H(x)+G(x)\,u,$

so that energy routing, dissipation, and port injection are built into the transition model itself (Reichhardt et al., 2017, Luan et al., 18 May 2026).

The same logic appears in classical nonequilibrium matter. In driven granular fluids, bulk kicks compensate collisional dissipation and maintain a homogeneous steady state with a well-defined granular temperature; in localized-drive diffusion, a single biased bond generates a Poisson problem with a source-sink structure; in dynamic material memory, the drive is encoded as an orbit in the $(\Omega,\dot{\Omega})$ plane, and switching depends on how that orbit crosses threshold curves (Kranz et al., 2010, Sadhu et al., 2011, Gutierrez-Prieto et al., 22 Aug 2025).

This breadth has an immediate consequence. PhysDrive does not imply that all driven systems share a universal reduced description. The granular-fluid analysis explicitly states that driven granular dynamics is not dynamically universal in the mode-coupling sense, because long-time behavior depends explicitly on the restitution coefficient through the memory prefactor $A_k(e)$, and PH-Dreamer states that its PH constraints act as auxiliary biases rather than formal closed-loop guarantees (Kranz et al., 2010, Luan et al., 18 May 2026).

2. Driven nonequilibrium media

In "Glass Transition for Driven Granular Fluids" (Kranz et al., 2010), PhysDrive is realized as homogeneous bulk driving of dissipative hard spheres. The system consists of $N$ identical hard spheres with binary collisions characterized by a normal restitution coefficient $e$, while neighboring pairs receive opposite random kicks to conserve momentum locally. Within a mode-coupling-theory construction, the normalized density correlator $\phi_k(t)$ obeys a Mori-Zwanzig-type equation with a positive memory kernel, and the long-time limit $f_k=\lim_{t\to\infty}\phi_k(t)$ satisfies the standard nonergodicity self-consistency equation. The central prediction is an ideal glass transition at a finite packing fraction for all $0\le e\le 1$, with the critical packing fraction $\pm x$0 increasing as $\pm x$1 decreases. The approach also recovers the canonical two-step relaxation scenario, the critical law $\pm x$2, the von Schweidler law in the early $\pm x$3 regime, and the divergence

$\pm x$4

At the same time, the paper emphasizes non-equilibrium specificity: detailed balance is broken, fluctuation-dissipation relations are violated, and equilibrium Newtonian or Brownian rescalings do not collapse the driven granular data (Kranz et al., 2010).

A distinct but closely related PhysDrive mechanism appears in "Long-range steady state density profiles induced by localized drive" (Sadhu et al., 2011). There, a single biased bond in an otherwise diffusive lattice acts as a dipole source for the steady-state density field. Away from the driven bond, the density satisfies a Laplace equation; at the bond endpoints, the continuity equation produces localized source and sink terms. The density deviation therefore maps onto the electrostatic potential of a dipole, giving algebraic rather than exponential spatial decay in two or higher dimensions. In $\pm x$5,

$\pm x$6

while in $\pm x$7 the decay is $\pm x$8. The associated stationary current has the structure of the dipole electric field. The same mapping survives exclusion interactions, with amplitudes renormalized by local correlations (Sadhu et al., 2011).

These two lines of work share a common interpretation. In the granular case, bulk drive stabilizes a nonequilibrium steady state in which glassy arrest remains sharply defined. In the localized-diffusion case, a microscopically local drive produces long-range steady-state organization. This suggests that PhysDrive can be either extensive, as in bulk temperature maintenance, or highly localized, as in a single driving bond, without losing predictive control over far-from-equilibrium structure.

3. Collective transport and dynamical phases

In "Velocity Force Curves, Laning, and Jamming for Oppositely Driven Disk Systems" (Reichhardt et al., 2017), PhysDrive appears as a species-dependent body force in an athermal overdamped disk mixture. For equal populations driven oppositely and for $\pm x$9, four nonequilibrium phases emerge as the drive $\dot{x}=[J(x)-R(x)]\,\nabla_x H(x)+G(x)\,u,$0 increases: a jammed crystalline cluster, a completely phase-separated collisionless state, a continuously mixing fluctuating phase, and a laning smectic state. At $\dot{x}=[J(x)-R(x)]\,\nabla_x H(x)+G(x)\,u,$1, the reported boundaries are $\dot{x}=[J(x)-R(x)]\,\nabla_x H(x)+G(x)\,u,$2 for phase I, $\dot{x}=[J(x)-R(x)]\,\nabla_x H(x)+G(x)\,u,$3 for phase II, $\dot{x}=[J(x)-R(x)]\,\nabla_x H(x)+G(x)\,u,$4 for phase III, and $\dot{x}=[J(x)-R(x)]\,\nabla_x H(x)+G(x)\,u,$5 for phase IV. The transitions are encoded directly in the velocity-force curves. The I$\dot{x}=[J(x)-R(x)]\,\nabla_x H(x)+G(x)\,u,$6II transition produces a sharp jump in $\dot{x}=[J(x)-R(x)]\,\nabla_x H(x)+G(x)\,u,$7, the II$\dot{x}=[J(x)-R(x)]\,\nabla_x H(x)+G(x)\,u,$8III transition exhibits negative differential mobility, and the III$\dot{x}=[J(x)-R(x)]\,\nabla_x H(x)+G(x)\,u,$9IV transition restores nearly free flow. Structure-factor signatures evolve correspondingly from sixfold Bragg peaks to a liquid-like ring and then to smectic peaks. The collisionless phase-separated and laned states are absorbing states in the sense that interspecies contacts vanish and velocity fluctuations disappear; the jammed phase is also absorbing, although it is contact-rich (Reichhardt et al., 2017).

In "Dynamics and Nonmonotonic Drag for Individually Driven Skyrmions" (Reichhardt et al., 2021), the drive acts on a single skyrmion moving through a bath of other skyrmions. The modified Thiele equation,

$(\Omega,\dot{\Omega})$0

contains both dissipative and Magnus terms. This immediately changes the rheology. In the damping-dominated regime, the effective viscosity increases monotonically with density, and the driven skyrmion always slows relative to the single-particle limit. In the Magnus-dominated regime, the velocity becomes nonmonotonic in density and can exceed the single-particle value. For $(\Omega,\dot{\Omega})$1 at fixed $(\Omega,\dot{\Omega})$2, $(\Omega,\dot{\Omega})$3 peaks near $(\Omega,\dot{\Omega})$4 at approximately $(\Omega,\dot{\Omega})$5, while the total speed reaches approximately $(\Omega,\dot{\Omega})$6 and remains above the single-particle value across a broad density window. The measured skyrmion Hall angle starts near zero at threshold, increases with drive, and saturates toward the intrinsic Hall angle; at fixed drive, increasing density can simultaneously reduce the Hall angle and boost the speed. The proposed mechanism is a density imbalance $(\Omega,\dot{\Omega})$7 created transverse to the drive, which the Magnus term converts into an additional longitudinal component, summarized by

$(\Omega,\dot{\Omega})$8

Negative differential conductivity appears in $(\Omega,\dot{\Omega})$9 for sufficiently large $A_k(e)$0 (Reichhardt et al., 2021).

A common misconception is that stronger crowding must always increase drag. The skyrmion study shows that this is correct in overdamped or damping-dominated settings but fails once gyroscopic transport channels become relevant. The disk study shows an analogous point from a different angle: increasing drive can first destabilize ordered low-collision motion into a collisional phase before larger drive restores collisionless laning.

4. Derivative-space control and programmable material memory

"Dynamic driving enables independent control of material bits for targeted memory" (Gutierrez-Prieto et al., 22 Aug 2025) formulates PhysDrive as control in derivative space. The material bit is a pre-buckled, double-clamped elastic beam with binary states defined by buckling direction. The global control input is the disk angular velocity profile $A_k(e)$1, whose derivatives generate inertial forces with different dependencies: the centrifugal contribution scales as $A_k(e)$2, while the Euler contribution scales as $A_k(e)$3. Because different beams have different geometric sensitivities, they can be selectively switched by designing drive cycles whose orbits in the $A_k(e)$4 plane cross the appropriate switching curves $A_k(e)$5 and $A_k(e)$6 in the intended order and orientation (Gutierrez-Prieto et al., 22 Aug 2025).

The model used to rationalize these thresholds is a reduced-order von Mises-truss analogue with a central mass connected to two linear springs. In the rotating frame, the equilibrium conditions include the elastic spring forces and the inertial forces

$A_k(e)$7

A realizable target orbit must satisfy the directionality constraint

$A_k(e)$8

so only crossings oriented away from the origin can produce switching. The experiments show that two harmonic protocols with identical amplitude $A_k(e)$9 but different frequency can drive the same initial state $N$0 to $N$1 or to $N$2, depending on which side of the $N$3-$N$4 intersection the orbit traverses (Gutierrez-Prieto et al., 22 Aug 2025).

The most elaborate demonstration is a five-bit architecture designed so that a single clockwise orbit beginning and ending at $N$5 executes an erase-write sequence capable of producing an arbitrary target $N$6. The paper reports a library of orbits that writes all 26 five-bit strings used for uppercase-letter encoding and experimentally demonstrates the sequential writing of “ORBIT.” Each selected orbit was repeated five times with consistent switching behavior. A notable implication is that local one-by-one actuation is not required for independent control: global drive, if shaped in derivative space, can realize any-to-any transitions within a single cycle (Gutierrez-Prieto et al., 22 Aug 2025).

5. Quantum and strongly driven coherent systems

In "Driving induced many-body localization" (Bairey et al., 2017), PhysDrive is implemented as an oscillating linear potential applied to a weakly disordered one-dimensional interacting hardcore-boson chain. The static undriven model with $N$7 and $N$8 is ergodic at half filling. After a time-dependent gauge transformation, the drive dresses the hopping by a Peierls phase, and high-frequency averaging yields the effective hopping

$N$9

Tuning $e$0 near a zero of $e$1 suppresses tunneling and enhances the relative strength of disorder and interactions. Numerically, the system enters a Floquet-MBL phase above a critical frequency and within a finite amplitude window around the first Bessel zero. The quasienergy level-spacing ratio crosses from the Wigner-Dyson value $e$2 toward the Poisson value $e$3, and the long-time imbalance saturates near $e$4 at $e$5 tuned to $e$6. The reported critical frequency is $e$7 at the first root and $e$8 near the second root. The result is important because periodic drive more often destabilizes localization, whereas here a specific coherent suppression of tunneling induces it (Bairey et al., 2017).

In "Strong mechanical driving of a single electron spin" (Barfuss et al., 2015), PhysDrive is realized without electromagnetic control fields. The system is a single NV center in a diamond cantilever, with electronic spin $e$9, zero-field splitting $\phi_k(t)$0 GHz, and hyperfine splitting $\phi_k(t)$1 MHz. The relevant transverse strain coupling is

$\phi_k(t)$2

which drives the otherwise forbidden $\phi_k(t)$3 transition between $\phi_k(t)$4 and $\phi_k(t)$5. For a classical coherent phonon field,

$\phi_k(t)$6

The experiment observes strain-driven Rabi oscillations with $\phi_k(t)$7 MHz at a tip displacement of approximately $\phi_k(t)$8 nm, mechanically induced Autler-Townes splittings, and beyond-RWA crossings and anticrossings as $\phi_k(t)$9 approaches and exceeds $f_k=\lim_{t\to\infty}\phi_k(t)$0. The maximum reported drive reaches $f_k=\lim_{t\to\infty}\phi_k(t)$1 MHz. Continuous dynamical decoupling in the dressed basis extends the Ramsey coherence time from $f_k=\lim_{t\to\infty}\phi_k(t)$2 to $f_k=\lim_{t\to\infty}\phi_k(t)$3. Residual dephasing is attributed to electric-field or strain noise, temperature drift of $f_k=\lim_{t\to\infty}\phi_k(t)$4, and second-order magnetic coupling (Barfuss et al., 2015).

These two studies delimit complementary quantum meanings of PhysDrive. One uses periodic forcing to renormalize an effective static Hamiltonian and access a Floquet-MBL phase; the other uses intrinsic strain to generate coherent strong driving and dressed-state protection. In both cases, the drive is not merely a perturbation but the central engineering handle.

6. Physics-structured learning and engineering control

"PH-Dreamer: A Physics-Driven World Model via Port-Hamiltonian Generative Dynamics" (Luan et al., 18 May 2026) brings PhysDrive into model-based reinforcement learning. The framework combines an RSSM backbone with a PH shadow transition on projected physical latents, an explicit kinematics-aware energy world model, and an energy-guided Actor-Critic regularized by Lagrangian multipliers. The explicit branch parameterizes

$f_k=\lim_{t\to\infty}\phi_k(t)$5

computes work and dissipation through $f_k=\lim_{t\to\infty}\phi_k(t)$6 and $f_k=\lim_{t\to\infty}\phi_k(t)$7, and supplies $f_k=\lim_{t\to\infty}\phi_k(t)$8 and $f_k=\lim_{t\to\infty}\phi_k(t)$9 to the policy objective. Across DeepMind Control Suite tasks, the reported asymptotic average return is $0\le e\le 1$0 for PH-Dreamer versus $0\le e\le 1$1 for R2Dreamer; imagined reward averages are $0\le e\le 1$2 versus $0\le e\le 1$3; latent log phase volume is reduced by $0\le e\le 1$4; energy consumption is reduced by up to $0\le e\le 1$5; and mean squared jerk is reduced by up to $0\le e\le 1$6. The paper explicitly notes, however, that the PH constraints are auxiliary and do not provide closed-loop guarantees, and that the explicit energy branch relies on proprioceptive inputs rather than pure pixel-based discovery (Luan et al., 18 May 2026).

A more classical control-theoretic PhysDrive appears in "Data Set Description: Identifying the Physics Behind an Electric Motor -- Data-Driven Learning of the Electrical Behavior (Part II)" (Hanke et al., 2020). The dataset contains approximately $0\le e\le 1$7 million samples from an IPMSM fed by a two-level IGBT inverter. Each row stores measured $0\le e\le 1$8 at controller-cycle instant $0\le e\le 1$9 together with $\pm x$00 at $\pm x$01, but successive rows do not form a continuous time series. The controller cycle is $\pm x$02, the prediction horizon is $\pm x$03, and the dataset spans $\pm x$04 current setpoints under $\pm x$05 V and $\pm x$06. The paper advocates per-vector linear or nonlinear discrete-time models, such as

$\pm x$07

and recommends class balancing over a grid in $\pm x$08 that yields $\pm x$09 valid classes per subset and approximately $\pm x$10 coverage at $\pm x$11 samples per class. The stated rationale is that learned models capture saturation, flux harmonics, inverter nonlinearity, dead-time, interlocking, and measurement offsets that nominal white-box models omit (Hanke et al., 2020).

"Driveability Constrained Models for Optimal Control of Hybrid Electric Vehicles" (Miretti et al., 2023) makes PhysDrive explicitly vehicular. For a P2 parallel hybrid, the stage cost augments fuel consumption with penalties on gear changes, engine starts, and used torque fraction:

$\pm x$12

Dynamic programming on Artemis cycles shows clear trade-offs. The baseline fuel-optimal strategy achieves $\pm x$13 L/100 km, $\pm x$14 shifts per minute, $\pm x$15 engine starts per minute, and average torque reserve $\pm x$16. Penalizing gear shifts reduces shifts to $\pm x$17 per minute at a fuel penalty of $\pm x$18; penalizing engine starts reduces starts to $\pm x$19 per minute at $\pm x$20 fuel; penalizing torque usage increases average reserve to $\pm x$21 at $\pm x$22 fuel. The paper’s practical conclusion is that driveability objectives can be encoded as explicit physics-grounded penalties and then distilled into real-time rules such as dwell-time constraints, gear hysteresis, and reserve targets (Miretti et al., 2023).

7. PhysDrive as a multimodal in-vehicle sensing dataset

In its most specific current usage, "PhysDrive: A Multimodal Remote Physiological Measurement Dataset for In-vehicle Driver Monitoring" (Wang et al., 25 Jul 2025) names a dataset for contactless physiological sensing in real driving. It includes synchronized RGB video, near-infrared video, and raw mmWave radar together with six physiological ground truths: ECG, BVP, respiration, HR, RR, and SpO$\pm x$23. The dataset comprises $\pm x$24 licensed drivers, evenly split by sex, aged $\pm x$25-$\pm x$26 years with mean $\pm x$27 and standard deviation $\pm x$28. Each driver contributes six segments of about five minutes, for a total of about $\pm x$29 hours and about $\pm x$30 km per driver. The design spans three vehicle classes, four illumination conditions, two driver-action conditions, and three road conditions. RGB is recorded at $\pm x$31 fps and $\pm x$32 resolution, NIR at $\pm x$33 fps and $\pm x$34, and radar at $\pm x$35 fps with effective bandwidth $\pm x$36 GHz, a $\pm x$37-antenna virtual array, range resolution of about $\pm x$38 cm, and angular resolution $\pm x$39 (Wang et al., 25 Jul 2025).

The benchmark protocol uses an $\pm x$40 cross-subject train-validation-test split over the $\pm x$41 drivers, with five independent runs. Evaluation employs MAE, RMSE, Pearson correlation, and SNR. The reported cross-subject HR results show a clear modality hierarchy in this dataset: for RGB, PhysNet reaches HR MAE $\pm x$42, RMSE $\pm x$43, and $\pm x$44; for NIR, PhysNet reaches HR MAE $\pm x$45, RMSE $\pm x$46, and $\pm x$47; for mmWave, mmFormer reaches HR MAE $\pm x$48, RMSE $\pm x$49, and $\pm x$50, with RR MAE $\pm x$51 and $\pm x$52. The paper also notes that radar waveform recovery lags behind direct HR and RR regression, plausibly because waveform recovery is more sensitive to residual temporal misalignment. SpO$\pm x$53 is included but not benchmarked because the distribution is narrow and no hypoxia induction was performed for safety (Wang et al., 25 Jul 2025).

The dataset is also explicit about its limitations. The participant pool is predominantly East Asian; passenger monitoring is outside scope; software-level synchronization leaves up to $\pm x$54 s drift; and the SpO$\pm x$55 channel lacks the variability needed for strong estimation benchmarks. Even so, the dataset makes PhysDrive a concrete shared benchmark as well as an abstract methodological theme: it operationalizes physics-aware multimodal sensing in a domain where illumination changes, motion, vibration, and vehicle-specific multipath are intrinsic rather than artificially suppressed (Wang et al., 25 Jul 2025).