Isometric fluctuation relations for equilibrium states with broken symmetry

Integration of Geostatistical and Sentinal-2AMultispectral Satellite Image Analysis for Predicting Soil Fertility Condition in Drylands

For modelling and predicting soil indicators to be fully operational and facilitate decision-making at any spatial level, there is a requirement for precise spatially referenced soil information to be available as input data. This paper focuses on showing the capacity of Sentinal-2A(S2A) multispectral imaging to predict soil properties and provide geostatistical analysis (ordinary kriging) for mapping dry land soil fertility conditions (SOCs). Conditioned Latin hypercube sampling was used to select the representative sampling sites within the study area. To achieve the objectives of this work, 48 surface soil samples were collected from the western part of Matrouh Governorate, Egypt, and pH, soil organic matter (SOM), available nitrogen (N), phosphorus (P), and potassium (K) levels were analyzed. Multilinear regression (MLR) was used to model the relationship between image reflectance and laboratory analysis (of pH, SOM, N, P, and K in the soil), followed by mapping the predicted outputs using ordinary kriging. Model fitting was achieved by removing variables according to the confidence level (95%).Around 30% of the samples were randomly selected to verify the validity of the results. The randomly selected samples helped express the variety of the soil characteristics from the investigated area. The predicted values of pH, SOM, N, P, and K performed well, with R2 values of 0.6, 0.7, 0.55, 0.6, and 0.92 achieved for pH, SOM, N, P, and K, respectively. The results from the ArcGIS model builder indicated a descending fertility order within the study area of: 70% low fertility, 22% moderate fertility, 3% very low fertility, and 5% reference terms. This work evidence that which can be predicted from S2A images and provides a reference for soil fertility monitoring in drylands. Additionally, this model can be easily applied to environmental conditions similar to those of the studied area.

Unified approach to classical speed limit and thermodynamic uncertainty relation

The total entropy production quantifies the extent of irreversibility in thermodynamic systems, which is nonnegative for any feasible dynamics. When additional information such as the initial and final states or moments of an observable is available, it is known that tighter lower bounds on the entropy production exist according to the classical speed limits and the thermodynamic uncertainty relations. Here we obtain a universal lower bound on the total entropy production in terms of probability distributions of an observable in the time forward and backward processes. For a particular case, we show that our universal relation reduces to a classical speed limit, imposing a constraint on the speed of the system's evolution in terms of the Hatano-Sasa entropy production. Notably, the obtained classical speed limit is tighter than the previously reported bound by a constant factor. Moreover, we demonstrate that a generalized thermodynamic uncertainty relation can be derived from another particular case of the universal relation. Our uncertainty relation holds for systems with time-reversal symmetry breaking and recovers several existing bounds. Our approach provides a unified perspective on two closely related classes of inequality: classical speed limits and thermodynamic uncertainty relations.

Symmetry-induced fluctuation relations for dynamical observables irrespective of their behavior under time reversal

We extend previous work to describe a class of fluctuation relations (FRs) that emerge as a consequence of symmetries at the level of stochastic trajectories in Markov chains. We prove that given such a symmetry, and for a suitable dynamical observable, it is always possible to obtain a FR under a biased dynamics corresponding to the so-called generalized Doob transform. The general transformations of the dynamics that we consider go beyond time-reversal or spatial isometries, and an implication is the existence of FRs for observables irrespective of their behavior under time reversal, for example for time-symmetric observables rather than currents. We further show how to deduce in the long-time limit these FRs from the symmetry properties of the generator of the dynamics. We illustrate our results with four examples that highlight the novel features of our work.

Infinite family of universal profiles for heat current statistics in Fourier's law

Using tools from large deviation theory, we study fluctuations of the heat current in a model of d-dimensional incompressible fluid driven out of equilibrium by a temperature gradient. We find that the most probable temperature fields sustaining atypical values of the global current can be naturally classified in an infinite set of curves, allowing us to exhaustively analyze their topological properties and to define universal profiles onto which all optimal fields collapse. We also compute the statistics of empirical heat current, where we find remarkable logarithmic tails for large current fluctuations orthogonal to the thermal gradient. Finally, we determine explicitly a number of cumulants of the current distribution, finding interesting relations between them.

Structure of the optimal path to a fluctuation

Macroscopic fluctuations have become an essential tool to understand physics far from equilibrium due to the link between their statistics and nonequilibrium ensembles. The optimal path leading to a fluctuation encodes key information on this problem, shedding light on, e.g., the physics behind the enhanced probability of rare events out of equilibrium, the possibility of dynamic phase transitions, and new symmetries. This makes the understanding of the properties of these optimal paths a central issue. Here we derive a fundamental relation which strongly constrains the architecture of these optimal paths for general d-dimensional nonequilibrium diffusive systems, and implies a nontrivial structure for the dominant current vector fields. Interestingly, this general relation (which encompasses and explains previous results) makes manifest the spatiotemporal nonlocality of the current statistics and the associated optimal trajectories.

Scaling Law for Irreversible Entropy Production in Critical Systems

We examine the Jarzynski equality for a quenching process across the critical point of second-order phase transitions, where absolute irreversibility and the effect of finite-sampling of the initial equilibrium distribution arise in a single setup with equal significance. We consider the Ising model as a prototypical example for spontaneous symmetry breaking and take into account the finite sampling issue by introducing a tolerance parameter. The initially ordered spins become disordered by quenching the ferromagnetic coupling constant. For a sudden quench, the deviation from the Jarzynski equality evaluated from the ideal ensemble average could, in principle, depend on the reduced coupling constant ε₀ of the initial state and the system size L. We find that, instead of depending on ε₀ and L separately, this deviation exhibits a scaling behavior through a universal combination of ε₀ and L for a given tolerance parameter, inherited from the critical scaling laws of second-order phase transitions. A similar scaling law can be obtained for the finite-speed quench as well within the Kibble-Zurek mechanism.

Weak additivity principle for current statistics in d dimensions

The additivity principle (AP) allows one to compute the current distribution in many one-dimensional nonequilibrium systems. Here we extend this conjecture to general d-dimensional driven diffusive systems, and validate its predictions against both numerical simulations of rare events and microscopic exact calculations of three paradigmatic models of diffusive transport in d=2. Crucially, the existence of a structured current vector field at the fluctuating level, coupled to the local mobility, turns out to be essential to understand current statistics in d>1. We prove that, when compared to the straightforward extension of the AP to high d, the so-called weak AP always yields a better minimizer of the macroscopic fluctuation theory action for current statistics.

Cycles, randomness, and transport from chaotic dynamics to stochastic processes

An overview of advances at the frontier between dynamical systems theory and nonequilibrium statistical mechanics is given. Sensitivity to initial conditions is a mechanism at the origin of dynamical randomness-alias temporal disorder-in deterministic dynamical systems. In spatially extended systems, sustaining transport processes, such as diffusion, relationships can be established between the characteristic quantities of dynamical chaos and the transport coefficients, bringing new insight into the second law of thermodynamics. With methods from dynamical systems theory, the microscopic time-reversal symmetry can be shown to be broken at the statistical level of description in nonequilibrium systems. In this way, the thermodynamic entropy production turns out to be related to temporal disorder and its time asymmetry away from equilibrium.

Nonequilibrium potential and fluctuation theorems for quantum maps

We derive a general fluctuation theorem for quantum maps. The theorem applies to a broad class of quantum dynamics, such as unitary evolution, decoherence, thermalization, and other types of evolution for quantum open systems. The theorem reproduces well-known fluctuation theorems in a single and simplified framework and extends the Hatano-Sasa theorem to quantum nonequilibrium processes. Moreover, it helps to elucidate the physical nature of the environment that induces a given dynamics in an open quantum system.