arXiv subjects

Jordan M. Horowitz

Publications and source records attributed to Jordan M. Horowitz.

At least 19 recordsLinked to original sources

arXiv2026

Work to insert a particle into an active fluid

The chemical potential is defined as the work to quasi-statically add a particle to an equilibrium system. Inspired by this definition, we investigate how the work to add a particle to an active fluid depends on the activity, density, and insertion protocol. We find that the average work is protocol dependent and decreases with activity. Moreover, the work fluctuations retain asymmetric non-Gaussian tails even for slow particle insertions. We then compare the average particle-insertion work to the steady-state densities observed when two active fluids are brought into diffusive contact and observe opposing trends between density and work.

cond-mat.stat-mech↗

arXiv2024

Thermodynamic constraints on kinetic perturbations of homogeneous driven diffusions

We analyze the static response to kinetic perturbations of nonequilibrium steady states that can be modeled as diffusions. We demonstrate that kinetic response is purely a nonequilibirum effect, measuring the degree to which the Fluctuation-Dissipation Theorem is violated out of equilibrium. For driven diffusions in a flat landscape, we further demonstrate that such response is constrained by the strength of the nonequilibrium driving via quantitative inequalities.

cond-mat.stat-mech↗

arXiv2023

Dissipative timescales from coarse-graining irreversibility

We propose and investigate a method for identifying timescales of dissipation in nonequilibrium steady states modeled as discrete-state Markov jump processes. The method is based on how the irreversibility-measured by the statistical breaking of time-reversal symmetry-varies under temporal coarse-graining. We observe a sigmoidal-like shape of the irreversibility as a function of the coarse-graining time whose functional form we derive for systems with a fast driven transition. This theoretical prediction allows us to develop a method for estimating the dissipative time scale from time-series data by fitting estimates of the irreversibility to our predicted functional form. We further analyze the accuracy and statistical fluctuations of this estimate.

cond-mat.stat-mech↗

arXiv2023

Topologically-constrained fluctuations and thermodynamics regulate nonequilibrium response

Limits on a system's response to external perturbations inform our understanding of how physical properties can be shaped by microscopic characteristics. Here, we derive constraints on the steady-state nonequilibrium response of physical observables in terms of the topology of the microscopic state space and the strength of thermodynamic driving. Notably, evaluation of these limits requires no kinetic information beyond the state-space structure. When applied to models of receptor binding, we find that sensitivity is bounded by the steepness of a Hill function with a Hill coefficient enhanced by the chemical driving beyond the structural equilibrium limit.

cond-mat.stat-mech↗

arXiv2023

Trade-offs between number fluctuations and response in nonequilibrium chemical reaction networks

We study the response of chemical reaction networks driven far from equilibrium to logarithmic perturbations of reaction rates. The response of the mean number of a chemical species is observed to be quantitively limited by number fluctuations as well as the maximum thermodynamic driving force. We prove these trade-offs for linear chemical reaction networks and a class of nonlinear chemical reaction networks with a single chemical species. Numerical results for several model systems support the conclusion that these trade-offs continue to hold for a broad class of chemical reaction networks, though their precise form appears to depend sensitively on the deficiency of the network.

cond-mat.stat-mech↗

arXiv2022

On the Einstein relation between mobility and diffusion coefficient in an active bath

An active bath, made of self-propelling units, is a nonequilibrium medium in which the Einstein relation $D=μk_B T$ between the mobility $μ$ and the diffusivity $D$ of a tracer particle cannot be expected to hold a priori. We consider here heavy tracers for which these coefficients can be related to correlation functions which we estimate. We show that, to a good approximation, an Einstein relation does hold in an active bath upon using a different temperature which is defined mechanically, through the pressure exerted on the tracer.

cond-mat.stat-mech↗

arXiv2022

Comment on "Inferring broken detailed balance in the absence of observable currents"

In this reply, we resolve the apparent discrepancy raised in the "Comment on Inferring broken detailed balance in the absence of observable currents" [arXiv:2112.08978v1]. We stress that the non-instantaneous transition paths originate from the choice of a decimation process non-local in time, in contrast to the decimation process described in our original work, which commutes with time-reversal. Therefore, the example using such a non-local decimation procedure, which indeed gives rise to spurious time-irreversibility, does not invalidate our main result, which was rigorously derived and proven mathematically. We hope this reply highlights the subtlety of the different choices for decimating time series data which is pivotal for a correct understanding of the thermodynamics of small systems.

cond-mat.stat-mech↗

arXiv2022

Thermodynamic constraints on the nonequilibrium response of one-dimensional diffusions

We analyze the static response to perturbations of nonequilibrium steady states that can be modeled as one-dimensional diffusions on the circle. We demonstrate that an arbitrary perturbation can be broken up into a combination of three specific classes of perturbations that can be fruitfully addressed individually. For each class, we derive a simple formula that quantitatively characterizes the response in terms of the strength of nonequilibrium driving valid arbitrarily far from equilibrium.

cond-mat.stat-mech↗

arXiv2021

Size limits sensitivity in all kinetic schemes

Living things benefit from exquisite molecular sensitivity in many of their key processes, including DNA replication, transcription and translation, chemical sensing, and morphogenesis. At thermodynamic equilibrium, the basic biophysical mechanism for sensitivity is cooperative binding, for which it can be shown that the Hill coefficient, a sensitivity measure, cannot exceed the number of binding sites. Generalizing this fact, we find that for any kinetic scheme, at or away from thermodynamic equilibrium, a very simple structural quantity, the size of the support of a perturbation, always limits the effective Hill coefficient. This support bound sheds light on and unifies diverse sensitivity mechanisms, ranging from kinetic proofreading to a nonequilibrium Monod-Wyman-Changeux (MWC) model proposed for the E. coli flagellar motor switch, and represents a simple, precise bridge between experimental observations and the models we write down. In pursuit of mechanisms that saturate the support bound, we find a nonequilibrium binding mechanism, nested hysteresis, with sensitivity exponential in the number of binding sites, with implications for our understanding of models of gene regulation.

cond-mat.stat-mech↗

arXiv2021

Nonequilibrium Green-Kubo relations for hydrodynamic transport from an equilibrium-like fluctuation-response equality

Near equilibrium, Green-Kubo relations provide microscopic expressions for macroscopic transport coefficients in terms of equilibrium correlation functions. At their core, they are based on the intimate relationship between response and fluctuations as embodied by the equilibrium fluctuation-dissipation theorem, a connection generically broken far from equilibrium. In this work, we identify a class of perturbations whose response around far-from-equilibrium steady states is linked to steady-state correlation functions via an equilibrium-like fluctuation-response equality. We then utilize this prediction to substantiate linearized hydrodynamic transport equations that describe how spatial inhomogeneities in macroscopic nonequilibrium systems relax. As a consequence, we derive nonequilibrium Green-Kubo relations for the transport coefficients of two types of hydrodynamic variables: local conserved densities and broken-symmetry modes. A byproduct of this work is to provide a theoretical foundation for the validity of Onsager's regression hypothesis around nonequilibrium steady states. Our predictions are analytically and numerically corroborated for two model systems: density diffusion in a fluid of soft, spherical active Brownian particles and phase diffusion in the noisy Kuramoto model on a square lattice.

cond-mat.stat-mech↗

arXiv2021

Scale-dependent irreversibility in living matter

A defining feature of living matter is the ability to harness energy to self-organize multiscale structures whose functions are facilitated by irreversible nonequilibrium dynamics. While progress has been made in elucidating the underlying principles, what remains unclear is the role that thermodynamics plays in shaping these structures and their ensuing functions. Here, we unravel how a fundamental thermodynamic connection between the physical energy dissipation sustaining a nonequilibrium system and a measure of statistical irreversibility (arrow of time), can provide quantitative insight into the mechanisms of nonequilibrium activity across scales. Specifically, we introduce a multiscale irreversibility metric and demonstrate how it can be used to extract model-independent estimates of dissipative timescales. Using this metric, we measure the dissipation timescale of a multiscale cellular structure - the actomyosin cortex - and further observe that the irreversibility metric maintains a monotonic relationship with the underlying biological nonequilibrium activity. Additionally, the irreversibility metric can detect shifts in the dissipative timescales when we induce spatiotemporal patterns of biochemical signaling proteins upstream of actomyosin activation. Our experimental measurements are complemented by a theoretical analysis of a generic class of nonequilibrium dynamics, elucidating how dissipative timescales manifest in multiscale irreversibility.

physics.bio-ph↗

arXiv2020

Universal thermodynamic bounds on nonequilibrium response with biochemical applications

Diverse physical systems are characterized by their response to small perturbations. Near thermodynamic equilibrium, the fluctuation-dissipation theorem provides a powerful theoretical and experimental tool to determine the nature of response by observing spontaneous equilibrium fluctuations. In this spirit, we derive here a collection of equalities and inequalities valid arbitrarily far from equilibrium that constrain the response of nonequilibrium steady states in terms of the strength of nonequilibrium driving. Our work opens new avenues for characterizing nonequilibrium response. As illustrations, we show how our results rationalize the energetic requirements of two common biochemical motifs.

cond-mat.stat-mech↗

arXiv2019

Inferring broken detailed balance in the absence of observable currents

Identifying dissipation is essential for understanding the physical mechanisms underlying nonequilibrium processes. {In living systems, for example, the dissipation is directly related to the hydrolysis of fuel molecules such as adenosine triphosphate (ATP)}. Nevertheless, detecting broken time-reversal symmetry, which is the hallmark of dissipative processes, remains a challenge in the absence of observable directed motion, flows, or fluxes. Furthermore, quantifying the entropy production in a complex system requires detailed information about its dynamics and internal degrees of freedom. Here we introduce a novel approach to detect time irreversibility and estimate the entropy production from time-series measurements, even in the absence of observable currents. We apply our technique to two different physical systems, namely, a partially hidden network and a molecular motor. Our method does not require complete information about the system dynamics and thus provides a new tool for studying nonequilibrium phenomena.

cond-mat.stat-mech↗

arXiv2019

The Thermodynamic Uncertainty Relation in Biochemical Oscillations

Living systems regulate many aspects of their behavior through periodic oscillations of molecular concentrations, which function as `biochemical clocks.' These clocks are intrinsically subject to thermal fluctuations, so that the duration of a full oscillation cycle is random. Their success in carrying out their biological function is thought to depend on the degree to which these fluctuations in the cycle period can be suppressed. Biochemical oscillators also require a constant supply of free energy in order to break detailed balance and maintain their cyclic dynamics. For a given free energy budget, the recently discovered `thermodynamic uncertainty relation' yields the magnitude of period fluctuations in the most precise conceivable free-running clock. In this paper, we show that computational models of real biochemical clocks severely underperform this optimum, with fluctuations several orders of magnitude larger than the theoretical minimum. We argue that this suboptimal performance is due to the small number of internal states per molecule in these models, combined with the high level of thermodynamic force required to maintain the system in the oscillatory phase. We introduce a new model with a tunable number of internal states per molecule, and confirm that it approaches the optimal precision as this number increases.

physics.bio-ph↗

arXiv2019

Quantifying dissipation using fluctuating currents

Systems coupled to multiple thermodynamic reservoirs can exhibit nonequilibrium dynamics, breaking detailed balance to generate currents. To power these currents, the entropy of the reservoirs increases. The rate of entropy production, or dissipation, is a measure of the statistical irreversibility of the nonequilibrium process. By measuring this irreversibility in several biological systems, recent experiments have detected that particular systems are not in equilibrium. Here we discuss three strategies to replace binary classification (equilibrium versus nonequilibrium) with a quantification of the entropy production rate. To illustrate, we generate time-series data for the evolution of an analytically tractable bead-spring model. Probability currents can be inferred and utilized to indirectly quantify the entropy production rate, but this approach requires prohibitive amounts of data in high-dimensional systems. This curse of dimensionality can be partially mitigated by using the thermodynamic uncertainty relation to bound the entropy production rate using statistical fluctuations in the probability currents.

cond-mat.stat-mech↗

arXiv2019

Bacterial range expansions on a growing front: Roughness, Fixation, and Directed Percolation

Directed Percolation (DP) is a classic model for nonequilibrium phase transitions into a single absorbing state (fixation). It has been extensively studied by analytical and numerical techniques in diverse contexts. Recently, DP has appeared as a generic model for the evolutionary/ecological dynamics of competing bacterial populations. Range expansion -- the stochastic reproduction of bacteria competing for space to be occupied by their progeny -- leads to a fluctuating and rough growth front, which is known from experiment and simulation to affect the underlying critical behavior of the DP transition. In this work, we employ symmetry arguments to construct a pair of non-linear stochastic partial differential equations describing the co-evolution of surface roughness with the composition field of DP. Macroscopic manifestations (phenomenology) of these equations on growth patterns and genealogical tracks of range expansion are discussed; followed by a renormalization group analysis of possible scaling behaviors at the DP transition.

cond-mat.stat-mech↗

arXiv2019

Hysteretic thermodynamic uncertainty relation for systems with broken time-reversal symmetry

The thermodynamic uncertainty relation gives a lower bound on the amount of dissipation in a mesoscopic system. By considering the fluctuations in the hysteresis of the current -- the sum of the currents in the time-forward and time-reversed processes -- we extend this relation to systems with broken time-reversal symmetry, either due to the presence of odd state variables, odd driving field or due to explicit time-dependent driving that is time-reversal asymmetric. We illustrate our predictions on a dilute, weakly-interacting gas driven out of equilibrium by the slow compression of a piston and on a ballistic multi-terminal conductor with an external magnetic field.

cond-mat.stat-mech↗

arXiv2018

Quantum fluctuation theorems for arbitrary environments: adiabatic and non-adiabatic entropy production

We analyze the production of entropy along non-equilibrium processes in quantum systems coupled to generic environments. First, we show that the entropy production due to final measurements and the loss of correlations obeys a fluctuation theorem in detailed and integral forms. Second, we discuss the decomposition of the entropy production into two positive contributions, adiabatic and non-adiabatic, based on the existence of invariant states of the local dynamics. Fluctuation theorems for both contributions hold only for evolutions verifying a specific condition of quantum origin. We illustrate our results with three relevant examples of quantum thermodynamic processes far from equilibrium.

quant-ph↗