arXiv subjects

Swetamber Das

Publications and source records attributed to Swetamber Das.

14 recordsLinked to original sources

arXiv2026

Force Geometry and Irreversibility in Nonequilibrium Overdamped Dynamics

Recent experiments have revealed heterogeneous dissipation in optically trapped systems, often anticorrelated with local positional fluctuations, exposing a structural gap in the scalar stochastic thermodynamic description. While the scalar framework successfully quantifies dissipation through currents and entropy production rates, it does not reveal the underlying vectorial force geometry that shapes spatial dissipation patterns. Here, we bridge this gap by identifying force geometry as an organizing principle for nonequilibrium thermodynamics, introducing force alignment as a geometric determinant of irreversibility. We show that entropy production depends not only on force magnitudes but also on the relative orientation between deterministic driving forces and entropic gradients, vanishing only under exact anti-alignment with matched magnitudes. We formalize this geometric alignment through a time-dependent force-correlation coefficient, quantifying the relative orientation between the forces. This yields an instantaneous geometric lower bound on entropy production that remains valid even when force magnitudes are matched. For overdamped dynamics, perfect anti-alignment defines a thermodynamic stall where net transport vanishes and the lower bound on entropy production is saturated. This force-level perspective provides a structural explanation for the experimentally observed fluctuation-dissipation anticorrelation and nonuniform dissipation. We construct geometric control charts for both constant dragging and sinusoidal driving protocols, explicitly locating experimental operating points within this force-space representation. Together, these results position force geometry as a unifying structural perspective on irreversibility, spanning active biological systems, microrheology, and naturally extending to underdamped dynamics.

cond-mat.stat-mech↗

arXiv2026

Geometry- and inertia-limited chaotic growth in classical many-body systems

Chaotic instability in many-body systems is commonly quantified by the largest Lyapunov exponent, yet general constraints on its magnitude in classical interacting systems remain poorly understood. Here we establish explicit, Hamiltonian-specific upper bounds on the largest Lyapunov exponent for classical many-body systems with local interactions. These bounds arise from instantaneous stability constraints on the Hamiltonian flow and are expressed in terms of inertial scales and the curvature of the interaction potential. We show that they naturally separate into two qualitatively distinct classes: non-violable bounds, controlled by worst-case local curvature scales and inertia and insensitive to spatial structure, and ergodic ceilings, which retain spectral information and encode collective modes and finite-size effects under generic dynamical evolution. For a paradigmatic one-dimensional coupled-rotor chain (Josephson junction array), the ergodic ceiling admits a closed analytic form and produces a dynamically inaccessible region for sustained chaotic growth in the Lyapunov exponent-energy plane, which we confirm numerically. In contrast to non-violable estimates, the ergodic ceiling yields a sharper constraint on chaotic growth by capturing collective suppression mechanisms absent at the level of local curvature alone. Remarkably, in the thermodynamic limit the ergodic ceiling asymptotically approaches an inertial ceiling that limits sustained Lyapunov growth, becoming independent of temperature and interaction strength. While classical systems do not admit universal chaos bounds, our results identify a broad class of natural Hamiltonian systems in which chaotic growth is inherently limited by inertia and interaction geometry, thereby setting a minimal microscopic timescale for long-time loss of memory of initial conditions.

nlin.CD↗

arXiv2025

Phase space volume preserving dynamics for non-Hamiltonian systems

Infinitesimal volumes stretch and contract as they coevolve with classical phase space trajectories according to linearized dynamics. Unless these tangent-space dynamics are modified, chaotic evolution causes the volume spanned by evolving tangent vectors to collapse. However, this collapse is unphysical and due to their exponential alignment along the most expanding direction, independent of the compressibility of the phase-space volume. Here, we propose an alternative linearized dynamics and rectify the generalized Liouville equation to preserve phase space volume, even for non-Hamiltonian systems. Within a classical density matrix theory, we define the time evolution operator from the anti-symmetric part of the stability matrix so that phase space volume is time-invariant. The operator generates orthogonal transformations without distorting volume elements, providing an invariant measure for dissipative dynamics and a evolution equation for the density matrix akin to the quantum mechanical Liouville-von Neumann equation. The compressibility of volume elements is determined by a non-orthogonal operator made from the symmetric part of the stability matrix. We analyze complete sets of basis vectors for the tangent space dynamics of chaotic systems, which may be dissipative, transient or driven, without re-orthogonalization of tangent vectors. The linear harmonic oscillator, the Lorenz-Fetter model, and the H\'enon-Heiles system demonstrate the computation of the instantaneous Lyapunov exponent spectrum and the local Gibbs entropy flow rate using these bases and show that it is numerically convenient.

nlin.CD↗

arXiv2025

Dynamical system analysis of quantum tunneling in an asymmetric double-well potential

We study quantum tunneling in an asymmetric double-well potential using a dynamical systems--based approach rooted in the Ehrenfest formalism. In this framework, the time evolution of a Gaussian wave packet is governed by a hierarchy of coupled equations linking lower- and higher-order position moments. An approximate closure scheme, required to render the system tractable, yields a reduced dynamical system for the mean and variance, with skewness explicitly entering due to the potential's asymmetry. Stability analysis of this system identifies energy thresholds for detectable tunneling across the barrier and reveals regimes where tunneling, though theoretically allowed, remains practically undetectable. Comparison with full numerical solutions of the time-dependent Schr\"odinger equation shows that, beyond reproducing key tunneling features, the dynamical systems approach provides an interpretable description of quantum transport through tunneling in an effective asymmetric two-level system.

quant-ph↗

arXiv2025

Phase space contraction rate for classical mixed states

Physical systems with non-reciprocal or dissipative forces evolve according to a generalization of Liouville's equation that accounts for the expansion and contraction of phase space volume. Here, we connect geometric descriptions of these non-Hamiltonian dynamics to a recently established classical density matrix theory. In this theory, the evolution of a ``maximally mixed'' classical density matrix is related to the well-known phase space contraction rate that, when ensemble averaged, is the rate of entropy exchange with the surroundings. Here, we extend the definition of mixed states to include statistical and mechanical components, describing both the deformations of local phase space regions and the evolution of ensembles within them. As a result, the equation of motion for this mixed state represents the rate of contraction for an ensemble of dissipative trajectories. Recognizing this density matrix as a covariance matrix, its contraction rate is another measure of entropy flow characterizing nonequilibrium steady states.

cond-mat.stat-mech↗

arXiv2025

Spectral bounds on the entropy flow rate and Lyapunov exponents in differentiable dynamical systems

Some microscopic dynamics are also macroscopically irreversible, dissipating energy and producing entropy. For many-particle systems interacting with deterministic thermostats, the rate of thermodynamic entropy dissipated to the environment is the average rate at which phase space contracts. Here, we use this identity and the properties of a classical density matrix to derive upper and lower bounds on the entropy flow rate with the spectral properties of the local stability matrix. These bounds are an extension of more fundamental bounds on the Lyapunov exponents and phase space contraction rate of continuous-time dynamical systems. They are maximal and minimal rates of entropy production, heat transfer, and transport coefficients set by the underlying dynamics of the system and deterministic thermostat. Because these limits on the macroscopic dissipation derive from the density matrix and the local stability matrix, they are numerically computable from the molecular dynamics. As an illustration, we show that these bounds are on the electrical conductivity for a system of charged particles subject to an electric field.

physics.class-ph↗

arXiv2023

Classical Fisher information for differentiable dynamical systems

Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a form of uncertainty: Infinitesimal perturbations to the initial conditions can grow exponentially in time, a signature of deterministic chaos. As a measure of this uncertainty, we introduce another classical information, specifically for the deterministic dynamics of isolated, closed, or open classical systems not subject to noise. This classical measure of information is defined with Lyapunov vectors in tangent space, making it less akin to the classical Fisher information and more akin to the quantum Fisher information defined with wavevectors in Hilbert space. Our analysis of the local state space structure and linear stability lead to upper and lower bounds on this information, giving it an interpretation as the net stretching action of the flow. Numerical calculations of this information for illustrative mechanical examples show that it depends directly on the phase space curvature and speed of the flow.

physics.class-ph↗

arXiv2023

Maximum speed of dissipation

We derive statistical-mechanical speed limits on dissipation from the classical, chaotic dynamics of many-particle systems. In one, the rate of irreversible entropy production in the environment is the maximum speed of a deterministic system out of equilibrium, $\bar S_e/k_B\geq 1/2\Delta t$, and its inverse is the minimum time to execute the process, $\Delta t\geq k_B/2\bar S_e$. Starting with deterministic fluctuation theorems, we show there is a corresponding class of speed limits for physical observables measuring dissipation rates. For example, in many-particle systems interacting with a deterministic thermostat, there is a trade-off between the time to evolve between states and the heat flux, $\bar{Q}\Delta t\geq k_BT/2$. These bounds constrain the relationship between dissipation and time during nonstationary process, including transient excursions from steady states.

cond-mat.stat-mech↗

arXiv2022

Speed limits on classical chaos

Uncertainty in the initial conditions of dynamical systems can cause exponentially fast divergence of trajectories, a signature of deterministic chaos. Here, we derive a classical uncertainty relation that sets a speed limit on the rates of local observables underlying this behavior. For systems with a time-invariant stability matrix, this general speed limit simplifies to classical analogues of the Mandelstam-Tamm versions of the time-energy uncertainty relation. This classical bound derives from our definition of Fisher information in terms of Lyapunov vectors on tangent space, analogous to the quantum Fisher information defined in terms of wavevectors on Hilbert space. This information measures fluctuations in local stability of the state space and sets a lower bound on the time of classical, dynamical systems to evolve between two distinguishable states. The bounds it sets apply to systems that are open or closed, conservative or dissipative, actively driven or passively evolving, and directly connect the geometries of phase space and information.

nlin.CD↗

arXiv2021

Density matrix formulation of dynamical systems

Physical systems that dissipate, mix and develop turbulence also irreversibly transport statistical density. In statistical physics, laws for these processes have a mathematical form and tractability that depends on whether the description is classical or quantum mechanical. Here, we establish a theory for density transport in any classical dynamical system that is analogous to the density matrix formulation of quantum mechanics. Defining states in terms of a classical density matrix leads to generalizations of Liouville's theorem and Liouville's equation, establishing an alternative computationally-tractable basis for nonequilibrium statistical mechanics. The formalism is complete with classical commutators and anti-commutators that embed measures of local instability and chaos and are directly related to Poisson brackets when the dynamics are Hamiltonian. It also recovers the traditional Liouville equation and the Liouville theorem by imposing trace preservation or Hamiltonian dynamics. Applying to systems that are driven, transient, dissipative, regular, and chaotic, this formalism has the potential for broad applications.

cond-mat.stat-mech↗

arXiv2019

Power-law trapping in the volume-preserving Arnold-Beltrami-Childress map

Understanding stickiness and power-law behavior of Poincaré recurrence statistics is an open problem for higher-dimensional systems, in contrast to the well-understood case of systems with two degrees-of-freedom. We study such intermittent behavior of chaotic orbits in three-dimensional volume-preserving systems using the example of the Arnold-Beltrami-Childress map. The map has a mixed phase space with a cylindrical regular region surrounded by a chaotic sea for the considered parameters. We observe a characteristic overall power-law decay of the cumulative Poincaré recurrence statistics with significant oscillations superimposed. This slow decay is caused by orbits which spend long times close to the surface of the regular region. Representing such long-trapped orbits in frequency space shows clear signatures of partial barriers and reveals that coupled resonances play an essential role. Using a small number of the most relevant resonances allows for classifying long-trapped orbits. From this the Poincaré recurrence statistics can be divided into different exponentially decaying contributions which very accurately explains the overall power-law behavior including the oscillations.

nlin.CD↗

arXiv2019

Controlling synchronization in coupled area-preserving maps using stickiness

Unidirectionally coupled area-preserving maps with a mixed phase space may show identical synchronization in the sticky neighborhood of the regular islands. We use this fact to devise numerical procedures to control (delay and expedite) the process of synchronization in two standard maps coupled under the Pecora-Carroll coupling scheme. The delay method is based on controlled kicking of trajectories away from synchronization traps for as long as necessary. The method to expedite the process is achieved by a parameter perturbation technique which rapidly drives the chaotic trajectories to synchronization traps in the sticky neighborhoods of regular islands. We also discuss the limitations of these methods.

nlin.CD↗

arXiv2017

Synchronization, phase slips and coherent structures in area-preserving maps

The problem of synchronization of coupled Hamiltonian systems exhibits interesting features due to the non-uniform or mixed nature (regular and chaotic) of the phase space. We study these features by investigating the synchronization of unidirectionally coupled area-preserving maps coupled by the Pecora-Carroll method. We find that coupled standard maps show complete synchronization for values of the nonlinearity parameter at which regular structures are still present in phase space. The distribution of synchronization times has a power law tail indicating long synchronization times for at least some of the synchronizing trajectories. With the introduction of coherent structures using parameter perturbation in the system, this distribution crosses over to exponential behavior, indicating shorter synchronization times, and the number of initial conditions which synchronize increases significantly, indicating an enhancement in the basin of synchronization. On the other hand, coupled blinking vortex maps display both phase synchronization and phase slips, depending on the location of the initial conditions. We discuss the implication of our results.

nlin.CD↗

arXiv2014

Dynamics of impurities in a three-dimensional volume-preserving map

We study the dynamics of inertial particles in three dimensional incompressible maps, as representations of volume preserving flows. The impurity dynamics has been modeled, in the Lagrangian framework, by a six-dimensional dissipative bailout embedding map. The fluid-parcel dynamics of the base map is embedded in the particle dynamics governed by the map. The base map considered for the present study is the Arnold-Beltrami-Childress (ABC) map. We consider the behavior of the system both in the aerosol regime, where the density of the particle is larger than that of the base flow, as well as the bubble regime, where the particle density is less than that of the base flow. The phase spaces in both the regimes show rich and complex dynamics with three type of dynamical behaviors - chaotic structures, regular orbits and hyperchaotic regions. In the one-action case, the aerosol regime is found to have periodic attractors for certain values of the dissipation and inertia parameters. For the aerosol regime of the two-action ABC map, an attractor merging and widening crises is identified using the bifurcation diagram and the spectrum of Lyapunov exponents. After the crisis an attractor with two parts is seen, and trajectories hop between these parts with period 2. The bubble regime of the embedded map shows strong hyperchaotic regions as well as crisis induced intermittency with characteristic times between bursts that scale as a power law behavior as a function of the dissipation parameter. Furthermore, we observe riddled basin of attraction and unstable dimension variability in the phase space in the bubble regime. The bubble regime in one-action shows similar behavior. This study of a simple model of impurity dynamics may shed light upon the transport properties of passive scalars in three dimensional flows. We also compare our results with those seen earlier in two dimensional flows.

nlin.CD↗