arXiv subjects

Lamberto Rondoni

Publications and source records attributed to Lamberto Rondoni.

At least 37 records · Page 2Linked to original sources

arXiv2023

Finite reservoirs and irreversibility corrections to Hamiltonian systems statistics

We consider several Hamiltonian systems perturbed by external agents, that preserve their Hamiltonian structure. We investigate the corrections to the canonical statistics resulting from coupling such systems with possibly large but finite reservoirs, and from the onset of processes breaking the time reversal symmetry. We analyze exactly solvable oscillators systems, and perform simulations of relatively more complex ones. This indicates that the standard statistical mechanical formalism needs to be adjusted, in the ever more investigated nano-scale science and technology. In particular, the hypothesis that heat reservoirs be considered infinite and be described by the classical ensembles is found to be critical when exponential quantities are considered, since the large size limit may not coincide with the infinite size canonical result. Furthermore, process-dependent emergent irreversibility affects ensemble averages, effectively frustrating, on a statistical level, the time reversal invariance of Hamiltonian dynamics, that is used to obtain numerous results.

cond-mat.stat-mech↗

arXiv2023

Coherent structures at the origin of time irreversibility in wall turbulence

Time irreversibility is a distinctive feature of non-equilibrium phenomena such as turbulent flows, where irreversibility is mainly associated with an energy cascade process. An Eulerian, multiscale analysis of time irreversibility in wall-bounded turbulence is proposed in this study, which differs from previous works relying on a Lagrangian approach and mainly focusing on homogeneous turbulence. Outcomes reveal a strong connection between irreversibility levels and coherent structures in both turbulent channel and boundary layer flows. In the near-wall region, irreversibility is directly related to the inner spectral peak originating from small-scale turbulent structures in the buffer layer. Conversely, stronger irreversibility is found in correspondence of the outer spectral peak originating from larger turbulent flow scales far from the wall. Our results represent a first effort to characterize Eulerian TI in wall-bounded turbulent flows, thus paving the way for new developments in wall-turbulence modeling and control accounting for broken temporal symmetry.

physics.flu-dyn↗

arXiv2023

Nonequilibrium fluctuations of global warming

While the warming trends of the Earth's mean temperature are evident at climatological scales, the local temperature at shorter timescales are highly fluctuating. In this letter we show that the probabilities of such fluctuations are characterized by a special symmetry typical of systems out of equilibrium. Their nearly universal properties are linked to the fluctuation theorem and reveal that the progressive warming is accompanied by growing asymmetry of temperature distributions. These statistics allow us to project the global temperature variability in the near future, in line with predictions from climate models, providing valuable information about future extremes.

physics.geo-ph↗

arXiv2023

Helmholtz Thermodynamics Beyond Hamiltonians: Including Walls, Pressure and Heat Flow

For 1D Hamiltonian systems with periodic solutions, Helmholtz formalism provides a tantalizing interpretation of classical thermodynamics, based on time integrals of purely mechanical quantities and without need of statistical description. Here we extend this approach to include heat flux and pressure at the walls, thereby enabling it to describe actual thermodynamic transformations, such as isothermal compressions and expansions. The presence of hard walls, which gives rise to non zero pressure, is justified by means of the virial theorem, while the heat fluxes are introduced as quasi-static limits of suitably thermostatted Hamiltonians. Particular attention is paid to generalizing the minimalist cases of the harmonic oscillator and elastic bouncer, which afford clear physical interpretations. With such extensions, a complete picture of thermodynamics emerges, amenable to cyclic transformations capable of producing mechanical work from heat, like the Carnot cycle.

cond-mat.stat-mech↗

arXiv2022

Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes

We investigate the stochastic behavior of the single-trajectory spectral density $S(ω,\mathcal{T})$ of several Gaussian stochastic processes, i.e., Brownian motion, the Ornstein-Uhlenbeck process, the Brownian gyrator model and fractional Brownian motion, as a function of the frequency $ω$ and the observation time $\mathcal{T}$. We evaluate in particular the variance and the frequency-frequency correlation of $S(ω,\mathcal{T})$ for different values of $ω$. We show that these properties exhibit different behaviors for different physical cases and can therefore be used as a sensitive probe discriminating between different kinds of random motion. These results may prove quite useful in the analysis of experimental data.

cond-mat.stat-mech↗

arXiv2022

Noise-to-signal ratio of single-trajectory spectral densities in centered Gaussian processes

We discuss the statistical properties of a single-trajectory power spectral density $S(ω,\mathcal{T})$ of an arbitrary real-valued centered Gaussian process $X(t)$, where $ω$ is the angular frequency and $\mathcal{T}$ the observation time. We derive a double-sided inequality for its noise-to-signal ratio and obtain the full probability density function of $S(ω,\mathcal{T})$. Our findings imply that the fluctuations of $S(ω,\mathcal{T})$ exceed its average value $μ(ω,\mathcal{T})$. This implies that using $μ(ω,\mathcal{T})$ to describe the behavior of these processes can be problematic. We finally evaluate the typical behavior of $S(ω,\mathcal{T})$ and find that it deviates markedly from the average $μ(ω,\mathcal{T})$ in most cases.

cond-mat.stat-mech↗

arXiv2022

Time Reversal Symmetry for Classical, Nonrelativistic Quantum and Spin Systems in Presence of Magnetic Fields

We extend to quantum mechanical systems results previously obtained for classical mechanical systems, concerning time reversibility in presence of a magnetic field. As in the classical case, results like the Onsager reciprocal relations are consequently obtained, without recourse to the Casimir modification. The quantum systems treated here are nonrelativistic, and are described by the Schr{ö}dinger equation or the Pauli equation. In particular, we prove that the spin-field interaction does not break the time reversal invariance (TRI) of the dynamics, and that it does not require additional conditions for such a symmetry to hold, compared to the spinless cases.

quant-ph↗

arXiv2021

Exact Response Theory and Kuramoto dynamics

The dynamics of Kuramoto oscillators is investigated in terms of the exact response theory based on the Dissipation Function, which has been introduced in the field of nonequilibrium molecular dynamics. While linear response theory is a cornerstone of nonequilibrium statistical mechanics, it does not apply, in general, to systems undergoing phase transitions. Indeed, even a small perturbation may in that case result in a large modification of the state. An exact theory is instead expected to handle such situations. The Kuramoto dynamics, which undergoes synchronization transitions, is thus investigated as a testbed for the exact theory mentioned above. A comparison between the two approaches shows how the linear theory fails, while the exact theory yields the correct response.

cond-mat.stat-mech↗

arXiv2021

Diffusion and escape from polygonal channels: extreme values and geometric effects

Polygonal billiards are an example of pseudo-chaotic dynamics, a combination of integrable evolution and sudden jumps due to conical singular points that arise from the corners of the polygons. Such pseudo-chaotic behaviour, often characterised by an algebraic separation of nearby trajectories, is believed to be linked to the wild dependence that particle transport has on the fine details of the billiard table. Here we address this relation through a detailed numerical study of the statistics of displacement in a family of polygonal channel billiards with parallel walls. We show that transport is characterised by strong anomalous diffusion, with a mean square displacement that scales in time faster than linear, and with a probability density of the displacement exhibiting exponential tails and ballistic fronts. In channels of finite length the distribution of first-passage times is characterised by fat tails, with a mean first-passage time that diverges when the aperture angle is rational. These findings have non trivial consequences for a variety of experiments.

cond-mat.stat-mech↗

arXiv2021

Deterministic model of battery, uphill currents and non-equilibrium phase transitions

We consider point particles in a table made of two circular cavities connected by two rectangular channels, forming a closed loop under periodic boundary conditions. In the first channel, a bounce--back mechanism acts when the number of particles flowing in one direction exceeds a given threshold $T$. In that case, the particles invert their horizontal velocity, as if colliding with vertical walls. The second channel is divided in two halves parallel to the first, but located in the opposite sides of the cavities. In the second channel, motion is free. We show that, suitably tuning the sizes of cavities, of the channels and of $T$, non--equilibrium phase transitions take place in the $N\rightarrow \infty$ limit. This induces a stationary current in the circuit, thus modeling a kind of battery, although our model is deterministic, conservative, and time reversal invariant.

cond-mat.stat-mech↗

arXiv2021

Blue Holes and Froude Horizons: Circular Shallow Water Profiles for Astrophysical Analogs

Interesting analogies between shallow water dynamics and astrophysical phenomena have offered valuable insight from both the theoretical and experimental point of view. To help organize these efforts, here we analyze systematically the hydrodynamic properties of backwater profiles of the shallow water equations with 2D radial symmetry. In contrast to the more familiar 1D case typical of hydraulics, %already for {even in} isentropic conditions, a solution with minimum-radius horizon for the flow emerges, similar to the black hole and white hole horizons, where the critical conditions of unitary Froude number provide a unidirectional barrier for surface waves. Beyond these time-reversible solutions, a greater variety of cases arises, when allowing for dissipation by turbulent friction and shock waves (i.e., hydraulic jumps) for both convergent and divergent flows. The resulting taxonomy of the base-flow cases may serve as a starting point for a more systematic analysis of higher-order effects linked, e.g., to wave propagation and instabilities, capillarity, variable bed slope, and rotation.

physics.flu-dyn↗

arXiv2021

Displacement Autocorrelation Functions for Strong Anomalous Diffusion: A Scaling Form, Universal Behavior, and Corrections to Scaling

Strong anomalous diffusion is characterized by asymptotic power-law growth of the moments of displacement, with exponents that do not depend linearly on the order of the moment. The exponents concerning small-order moments are dominated by random motion, while higher-order exponents grow by faster trajectories, such as ballistic excursions or "light fronts". Often such a situation is characterized by two linear dependencies of the exponents on their order. Here, we introduce a simple exactly solvable model, the Fly-and-Die (FnD) model, that sheds light on this behavior and on the consequences of light fronts on displacement autocorrelation functions in transport processes. We present analytical expressions for the moments and derive a scaling form that expresses the long-time asymptotics of the autocorrelation function $\langle x(t_1)\,x(t_2)\rangle$ in terms of the dimensionless time difference $(t_2-t_1)/t_1$. The scaling form provides a faithful collapse of numerical data for vastly different systems. This is demonstrated here for the Lorentz gas with infinite horizon, polygonal billiards with finite and infinite horizon, the Lévy-Lorentz gas, the Slicer Map, and Lévy walks. Our analysis also captures the system-specific corrections to scaling.

cond-mat.stat-mech↗

arXiv2020

On a possible nonequilibrium imprint in the cosmic background at low frequencies

The cosmic background radiation has been observed to deviate from the Planck law expected from a blackbody at $\sim$ 2.7 K at frequencies below $\sim 3$ GHz. We discuss the abundance of the low-energy photons from the perspective of nonequilibrium statistical mechanics. We propose a mechanism of stochastic frequency-diffusion, the counterpart to stochastic acceleration for charged particles in a turbulent plasma, to modify the standard Kompaneets equation. The resulting violation of the Einstein relation allows to take advantage of low-frequency localization and finally leads to photon cooling. The new equation predicts a frequency distribution in agreement with the absolute temperature measurements of the cosmic background radiation down to about 20 MHz, for which we offer here an updated compilation. In that sense, the so called 'space roar' we observe today is interpreted as a nonequilibrium echo of the early universe, and of nonequilibrium conditions in the primordial plasma more specifically.

astro-ph.CO↗

arXiv2020

Time-dependence of the effective temperatures of a two-dimensional Brownian gyrator with cold and hot components

We consider a model of a two-dimensional molecular machine - called Brownian gyrator - that consists of two coordinates coupled to each other and to separate heat baths at temperatures respectively $T_x$ and $T_y$. We consider the limit in which one component is passive, because its bath is "cold", $T_x \to 0$, while the second is in contact with a "hot" bath, $T_y > 0$, hence it entrains the passive component in a stochastic motion. We derive an asymmetry relation as a function of time, from which time dependent effective temperatures can be obtained for both components. We find that the effective temperature of the passive element tends to a constant value, which is a fraction of $T_y$, while the effective temperature of the driving component grows without bounds, in fact exponentially in time, as the steady-state is approached.

cond-mat.stat-mech↗

arXiv2020

Fluctuation relations for dissipative systems in constant external magnetic field: theory and molecular dynamics simulations

It has recently been pointed out that Hamiltonian particle systems in constant magnetic fields satisfy generalized time-reversal symmetries that enable to prove useful statistical relationships based on equilibrium phase-space probability distributions without the need to invert, as commonly considered necessary, the magnetic field. Among these relations, that hold without need of Casimir modifications, one finds the standard linear response Green-Kubo relations, and consequently the Onsager reciprocal relations. Going beyond linear response is also possible, for instance in terms of transient and steady state Fluctuation Relations (FRs). Here we highlight how the generalized time-reversal symmetries ensure that the (transient) FRs theory directly applies also for systems in external magnetic fields. Furthermore we show that transient FR can indeed be verified in nonequilibrium molecular dynamics simulations, for systems subjected to magnetic and electric fields, which are thermostatted à la Nosé-Hoover. The result is nontrivial because, since it is not immediate within which sizes and time scales the effects can actually be observable, it is not obvious what one may obtain by real molecular dynamics simulations.

cond-mat.stat-mech↗

arXiv2020

Necessary and sufficient conditions for time reversal symmetry in presence of magnetic fields

Time reversal invariance (TRI) of particles systems has many consequences, among~which the celebrated Onsager reciprocal relations, a milestone in Statistical Mechanics dating back to 1931. Because for a long time it was believed that (TRI) dos not hold in presence of a magnetic field, a modification of such relations was proposed by Casimir in 1945. Only in the last decade, the~strict traditional notion of reversibility that led to Casimir's work has been questioned. It was then found that other symmetries can be used, which allow the Onsager reciprocal relations to hold without modification. In this paper we advance this investigation for classical Hamiltonian systems, substantially increasing the number of symmetries that yield TRI in presence of a magnetic field. We~first deduce the most general form of a generalized time reversal operation on the phase space of such a system; secondly, we express sufficient conditions on the magnetic field which ensure TRI. Finally, we examine common examples from statistical mechanics and molecular dynamics. Our main result is that TRI holds in a much wider generality than previously believed, partially explaining why no experimental violation of Onsager relations has so far been reported.

cond-mat.stat-mech↗

arXiv2020

Coexistence of ballistic and Fourier regimes in the $β$-FPUT lattice

Commonly, thermal transport properties of one-dimensional systems are found to be anomalous. Here, we perform a numerical and theoretical study of the $β$-FPUT chain, considered a prototypical model for one-dimensional anharmonic crystals, in contact with thermostats at different temperatures. We give evidence that, in steady state conditions, the {\it local} wave energy spectrum can be naturally split into modes that are essentially ballistic (non-interacting or scarcely interacting) and kinetic modes (interacting enough to relax to local thermodynamic equilibrium). We show numerically that the well-known divergence of the energy conductivity is related to how the transition region between these two sets of modes shifts in $k$-space with the system size $L$, due to properties of the collision integral of the system. Moreover, we show that the kinetic modes are responsible for a macroscopic behavior compatible with Fourier's law. Our work sheds light on the long-standing problem of the applicability of standard thermodynamics in one-dimensional nonlinear chains, testbed for understanding the thermal properties of nanotubes and nanowires.

cond-mat.stat-mech↗

arXiv2020

Fluctuation relations for systems in constant magnetic field

The validity of the Fluctuation Relations (FR) for systems in a constant magnetic field is investigated. Recently introduced time-reversal symmetries that hold in presence of static electric and magnetic fields and of deterministic thermostats are used to prove the transient FR without invoking, as commonly done, inversion of the magnetic field. Steady-state FR are also derived, under the t-mixing condition. These results extend the predictive power of important statistical mechanics relations. We illustrate this via the non-linear response for the cumulants of the dissipation, showing how the new FR enable to determine analytically null cumulants also for systems in a single magnetic field.

cond-mat.stat-mech↗