arXiv subjects

Timur Aslyamov

Publications and source records attributed to Timur Aslyamov.

At least 19 recordsLinked to original sources

arXiv2026

Emergent Second Law for Time-Dependent Nonequilibrium States

For nonautonomous open systems described by macroscopic stochastic thermodynamics, we derive an emergent second law that constrains time-dependent macroscopic fluctuations by the entropy production along the most probable evolution under the time-reversed driving protocol. We show that this bound can be understood as a macroscopic consequence of the fluctuation theorem: the time reverse of this evolution provides a possible fluctuation path under the forward dynamics. In the linear-response and slow-driving regime, the bound becomes an equality to first order and generalizes the McLennan-Zubarev formula to the time-dependent probability density of nonautonomous systems with weak nonconservative affinities. We illustrate our results in a bistable system under sudden quenches and periodic driving.

cond-mat.stat-mech↗

arXiv2026

Identifying Non-Ideal Reaction-Diffusion Systems Unable to Maintain Diffusion Out-of-Equilibrium

We develop a general method, based on the construction of a kinetic potential serving as a Lyapunov function, to establish when diffusion necessarily equilibrates in non-ideal reaction-diffusion systems under arbitrary driving by autonomous homogeneous chemostats. This equilibration of diffusion implies vanishing diffusion currents and homogeneous chemical potentials, while reactions can remain far from equilibrium. Using this method, we generalize the results of J. Chem. Phys. 161, 174108 (2024) by relaxing some of the underlying assumptions. Specifically, we show that diffusion equilibrates in reaction-diffusion systems whose chemical reaction network is either pseudo-detailed balanced, with reaction fluxes controlled by the stoichiometry of reactants and products, or complex balanced, with reaction fluxes controlled only by the stoichiometry of the reactants. These different constraints on the reaction fluxes are shown to originate from the distinct stoichiometric properties of the two classes of networks.

cond-mat.stat-mech↗

arXiv2026

Dynamical Fluctuation-Response Relations

We derive exact dynamical fluctuation-response relations (FRRs) for time-integrated observables of any nonautonomous Markov jump process. The finite-time covariance splits into an initial variability and an integral of response kernels along the driven dynamics. The identity sharpens the dynamical response thermodynamic and kinetic uncertainty relations and fluctuation-response inequalities (FRIs). For autonomous processes, dynamical FRRs yield two complementary frequency-domain relations. Steady-state FRRs are recovered in the long time limit, along with the fluctuation-dissipation theorem and Onsager reciprocity for detailed-balance dynamics. The importance of initial variability for slowly relaxing systems is also highlighted.

cond-mat.stat-mech↗

arXiv2026

Classification of instabilities for the nonideal Brusselator model

We investigate a nonideal, thermodynamically consistent Brusselator reaction-diffusion (RD) system that explicitly incorporates molecular interactions among species in both the diffusion process and the underlying chemical reaction network. Within this framework, we systematically revisit the Cross-Hohenberg classification of instabilities to assess the feasibility and characteristics of the various types of instability arising from the interplay between entropic and energetic contributions. Our analysis demonstrates that only type I and type III instabilities (the Cross-Hohenberg classification) can occur in this system; Energetic contributions do not explicitly generate instabilities, but may implicitly control their occurrence through their influence on the fixed-point (steady-state) concentrations. In cases where instabilities of different types coexist, we show that the resulting patterns are highly sensitive to the relative strengths of the competing instabilities.

cond-mat.stat-mech↗

arXiv2025

Faradaic and capacitive charging of an electrolyte-filled pore in response to a small applied potential

Electrochemical devices often charge both through Faradaic reactions and electric double layer formation. Here, we study these coupled processes in a model system of a long electrolyte-filled pore subject to a small suddenly-applied potential, close to the equilibrium potential $\Psi^\text{eq}$ at which there is no net Faradaic charge transfer. Specifically, we solve the coupled Poisson-Nernst-Planck and Frumkin-Butler-Volmer equations by asymptotic approximations, using the pore's small inverse aspect ratio as the small parameter. In the early-time limit, the reaction-diffusion equations yield an extended Faradaic transmission line model that includes a voltage source, $\Psi_\text{eq}$, biasing the Faradaic reactions, captured by the resistance $R_F$. In the long-time limit, the model exhibits a nontrivial potential of zero charge, $\Psi_\text{pzc} = \Psi_\text{eq}[1 - \hat{Z}(0)/R_F]$, where $\hat{Z}(0)$ is the experimentally accessible zero-frequency impedance of the system. This expression provides a new means to experimentally measure the Faradaic contribution to $\Psi_\text{pzc}$.

cond-mat.stat-mech↗

arXiv2025

Macroscopic fluctuation-response theory and its use for gene regulatory networks

Gaussian macroscopic fluctuation theory underpins the understanding of noise in a broad class of nonequilibrium systems. We derive exact fluctuation-response relations linking the power spectral density of stationary fluctuations to the linear response of stable nonequilibrium steady states. Both of these can be determined experimentally and used to reconstruct the kernel of the linearized dynamics and the diffusion matrix, and thus any features of the Gaussian theory. We apply our theory to gene regulatory networks with negative feedback, and derive an explicit internal-external noise decomposition of the power spectral density for any networks, including cross-correlations.

cond-mat.stat-mech↗

arXiv2025

Integrated covariances as excess observables weighted by currents and activities

Near equilibrium, the symmetric part of the time-integrated steady-state covariance, i.e., the time integral of correlation functions, is governed by the fluctuation-dissipation theorem, while the antisymmetric part vanishes due to Onsager reciprocity. Far from equilibrium, where these principles no longer apply, we develop a unified formalism for both symmetric and antisymmetric components of integrated covariances. We derive exact, computationally tractable expressions for these quantities, valid in arbitrary nonequilibrium steady states of Markov jump processes and Fokker--Planck equation. Both components are expressed in terms of excess observables, a notion central to both statistical physics and reinforcement learning. Furthermore, we establish thermodynamic upper bounds for antisymmetric covariances in terms of (pseudo-)entropy production and cycle affinities. Finally, we show that the speed up of self-averaging induced by nonequilibrium drivings which preserve kinetics (activity) is bounded by the cycle affinities (thermodynamic forces).

cond-mat.stat-mech↗

arXiv2025

Nonequilibrium fluctuation-response relations for state-current correlations

Recently, novel exact identities known as Fluctuation-Response Relations (FRRs) have been derived for nonequilibrium steady states of Markov jump processes. These identities link the fluctuations of state or current observables to a combination of responses of these observables to perturbations of transition rates. Here, we complement these results by deriving analogous FRRs applicable to mixed covariances of one state and one current observable. We further derive novel Inverse FRRs expressing individual state or current response in terms of a combination of covariances rather than vice versa. Using these relations, we demonstrate that the breaking of the Onsager symmetry requires the presence of state-current correlations. On the practical side, we demonstrate the applicability of FRRs for explaining the behavior of fluctuations in quantum dot devices or enzymatic reaction networks.

cond-mat.stat-mech↗

arXiv2024

Nonequilibrium fluctuation-response relations for state observables

Time-integrated state observables, which quantify the fraction of time spent by the system in a specific pool of states, are important in many fields, such as chemical sensing or the theory of fluorescence spectroscopy. We derive exact identities, called Fluctuation-Response Relations (FRRs), that connect the fluctuations of such observables to their response to external perturbations in nonequilibrium steady state of Markov jump processes. Using these results, we derive a first known upper bound on fluctuations of state observables, as well as some new lower bounds. We further demonstrate how our identities provide a deeper understanding of the mechanistic origin of fluctuations and reveal their properties dependent only on system topology, which may be relevant for model inference using measured data.

cond-mat.stat-mech↗

arXiv2024

Nonequilibrium Fluctuation-Response Relations: From Identities to Bounds

In nonequilibrium steady states of Markov jump processes, we derive exact Fluctuation-Response Relations (FRRs) that express the covariance between any pair of currents in terms of static responses in a notably simple form, thus generalizing the fluctuation-dissipation theorem far from equilibrium. We begin by considering perturbations in the symmetric part of the rates. We demonstrate that FRRs imply a hierarchy of thermodynamic bounds. These hierarchies prove the recently conjectured Response Thermodynamic Uncertainty Relation (R-TUR), which bounds the ratio between any current's response and its variance by the entropy production rate (EPR). We furthermore strengthen this bound in two distinct ways, using partial EPR in one case and pseudo-EPR in the other. For perturbations in the antisymmetric part of the rates, we show that the ratio between any current's response and its variance is bounded by traffic, a metric representing the total number of transitions per unit time in the system. As an application, we use FRRs to explain the origin of positive correlations between currents in Coulomb-blockaded systems previously observed in experiments.

cond-mat.stat-mech↗

arXiv2024

Nonequilibrium Thermodynamics of Non-Ideal Reaction-Diffusion Systems: Implications for Active Self-Organization

We develop a framework describing the dynamics and thermodynamics of open non-ideal reaction-diffusion systems, which embodies Flory-Huggins theories of mixtures and chemical reaction network theories. Our theory elucidates the mechanisms underpinning the emergence of self-organized dissipative structures in these systems. It evaluates the dissipation needed to sustain and control them, discriminating the contributions from each reaction and diffusion process with spatial resolution. It also reveals the role of the reaction network in powering and shaping these structures. We identify particular classes of networks in which diffusion processes always equilibrate within the structures, while dissipation occurs solely due to chemical reactions. The spatial configurations resulting from these processes can be derived by minimizing a kinetic potential, contrasting with the minimization of the thermodynamic free energy in passive systems. This framework opens the way to investigating the energetic cost of phenomena such as liquid-liquid phase separation, coacervation, and the formation of biomolecular condensates.

q-bio.MN↗

arXiv2024

Dissipation bounds precision of current response to kinetic perturbations

The precision of currents in Markov networks is bounded by dissipation via the so-called thermodynamic uncertainty relation (TUR). In our work, we demonstrate a similar inequality that bounds the precision of the static current response to perturbations of kinetic barriers. Perturbations of such type, which affect only the system kinetics but not the thermodynamic forces, are highly important in biochemistry and nanoelectronics. We prove that our inequality cannot be derived from the standard TUR. Instead, it implies the standard TUR and provides an even tighter bound for dissipation. We also provide a procedure for obtaining the optimal response precision for a given model.

cond-mat.stat-mech↗

arXiv2024

General Theory of Static Response for Markov Jump Processes

We consider Markov jump processes on a graph described by a rate matrix that depends on various control parameters. We derive explicit expressions for the static responses of edge currents and steady-state probabilities. We show that they are constrained by the graph topology (i.e. the incidence matrix) by deriving response relations (i.e. linear constraints linking the different responses) and topology-dependent bounds. For unicyclic networks, all scaled current responses are between zero and one and must sum to one. Applying these results to stochastic thermodynamics, we derive explicit expressions for the static response of fundamental currents (which carry the full dissipation) to fundamental thermodynamic forces (which drive the system away from equilibrium).

cond-mat.stat-mech↗

arXiv2024

Symmetry shapes thermodynamics of macroscopic quantum systems

We derive a systematic approach to the thermodynamics of quantum systems based on the underlying symmetry groups. We show that the entropy of a system can be described in terms of group-theoretical quantities that are largely independent of the details of its density matrix. We apply our technique to generic $N$ identical interacting $d$-level quantum systems. Using permutation invariance, we find that, for large $N$, entropy displays a universal large deviation behavior with a rate function $s(\boldsymbol{x})$ that is completely independent of the microscopic details of the model, but depends only on the size of the irreducible representations of the permutation group $\text{S}_N$. In turn, the partition function is shown to satisfy a large deviation principle with a free energy $f(\boldsymbol{x})=e(\boldsymbol{x})-\beta^{-1}s(\boldsymbol{x})$, where $e(\boldsymbol{x})$ is a rate function that only depends on the ground state energy of particular subspaces determined by group representation theory. We apply our theory to the transverse-field Curie-Weiss model, a minimal model of phase transition exhibiting an interplay of thermal and quantum fluctuations.

quant-ph↗

arXiv2023

Nonideal Reaction-Diffusion Systems: Multiple Routes to Instability

We develop a general classification of the nature of the instabilities yielding spatial organization in open nonideal reaction-diffusion systems, based on linear stability analysis. This encompasses dynamics where chemical species diffuse, interact with each other, and undergo chemical reactions driven out of equilibrium by external chemostats. We find analytically that these instabilities can be of two types: instabilities caused by intermolecular energetic interactions (E type), and instabilities caused by multimolecular out-of-equilibrium chemical reactions (R type). Furthermore, we identify a class of chemical reaction networks, containing unimolecular networks but also extending beyond them, that can only undergo E-type instabilities. We illustrate our analytical findings with numerical simulations on two reaction-diffusion models, each displaying one of the two types of instability and generating stable patterns.

cond-mat.stat-mech↗

arXiv2023

Equivalent circuit and continuum modeling of the impedance of electrolyte-filled pores

Batteries, supercapacitors, and several other electrochemical devices charge by accumulating ions in the pores of electrolyte-immersed porous electrodes. The charging of such devices has long been interpreted using equivalent circuits and the partial differential equations these give rise to. Here, we discuss the validity of the transmission line (TL) circuit and equation for modeling a single electrolyte-filled pore in contact with a reservoir of resistance $R_{r}$. The textbook derivation of the pore-reservoir impedance $R_r+Z_p$ from the TL equation does not correctly account for ionic current conservation at the pore-reservoir interface. However, correcting this shortcoming leads to the same impedance. We also show that the pore impedance $Z_p$ can be derived directly from the TL circuit, bypassing the TL equation completely. The TL circuit assumes equipotential lines in an electrolyte-filled pore to be straight, which is not the case near the pore entrance and end. To determine the importance of these regions, we numerically simulated the charging of pores of different lengths $\ell_p$ and radii $\varrho_p$ through the Poisson-Nernst-Planck equations. We find that pores with aspect ratios beyond $\ell_p/\varrho_p\gtrapprox5$ have impedances in good agreement with $Z_p$.

cond-mat.soft↗

arXiv2023

Nonequilibrium Response for Markov Jump Processes: Exact Results and Tight Bounds

Generalizing response theory of open systems far from equilibrium is a central quest of nonequilibrium statistical physics. Using stochastic thermodynamics, we develop an algebraic method to study the response of nonequilibrium steady state to arbitrary perturbations. This allows us to derive explicit expressions for the response of edge currents as well as traffic to perturbations in kinetic barriers and driving forces. We also show that these responses satisfy very simple bounds. For the response to energy perturbations, we straightforwardly recover results obtained using nontrivial graph-theoretical methods.

cond-mat.stat-mech↗

arXiv2022

Analytical solution to the Poisson-Nernst-Planck equations for the charging of a long electrolyte-filled slit pore

We study the charging dynamics of a long electrolyte-filled slit pore in response to a suddenly applied potential. In particular, we analytically solve the Poisson-Nernst-Planck (PNP) equations for a pore for which $λ_D\ll H\ll L$, with $λ_D$ the Debye length and $H$ and $L$ the pore's width and length. For small applied potentials, we find the time-dependent potential drop between the pore's surface and its center to be in complete agreement with a prediction of the celebrated transmission line model. For moderate to high applied potentials, prior numerical work showed that charging slows down at late times; Our analytical model reproduces and explains such biexponential charge buildup.

cond-mat.soft↗