arXiv subjects

Richard E. Spinney

Publications and source records attributed to Richard E. Spinney.

14 recordsLinked to original sources

arXiv2025

Stochastic Multistability of Clonallike States in the Eigen Model: a Fidelity Catastrophe

The Eigen model is a prototypical toy model of evolution that is synonymous with the so-called error catastrophe: when mutation rates are sufficiently high, the genetic variant with the largest replication rate does not occupy the largest fraction of the total population because it acts as a source for the other variants. Here we show that, in the stochastic version of the Eigen model, there is also a fidelity catastrophe. This arises due to the state-dependence of fluctuations and occurs when rates of mutation fall beneath a certain threshold, which we calculate. The result is a type of noise-induced multistability whereupon the system stochastically switches between short-lived regimes of effectively clonal behavior by different genetic variants. Most notably, when the number of possible variants -- typically $\sim4^L$, with $L\gg 1$ the length of the genome -- is significantly larger than the population size, there is only a vanishingly small interval of mutation rates for which the Eigen model is neither in the fidelity- nor error-catastrophe regimes, seemingly subverting traditional expectations for evolutionary systems.

q-bio.PE↗

arXiv2025

Non-Stationary Critical Phenomena: Expanding The Critical Point

A prototypical model of symmetry-broken active matter -- biased quorum-sensing active particles (bQSAPs) -- is used to extend notions of dynamic critical phenomena to the paradigmatic setting of driven transport, where characteristic behaviours are nonstationary and involve persistent fluxes. To do so, we construct an effective field theory with a single order-parameter -- a nonstationary analogue of active Model B -- that reflects the fact that different properties of bQSAPs can only be interpreted in terms of passive thermodynamics in appropriately chosen inertial frames. This codifies the movement of phase boundaries due to nonequilibrium fluxes between coexisting bulk phases in terms of a difference in effective chemical potentials and therefore an {\it unequal} tangent construction on a bulk free energy density. The result is both an anomalous form of coarsening and, more generally, an exotic phase structure; binodals are permitted to cross spinodal lines so that criticality is no longer constrained to a single point. Instead, criticality, with exponents that are seemingly unchanged from symmetric QSAPs, is shown to exist along a line that marks the entry to an otherwise forbidden region of phase space. The interior of this region is not critical in the conventional sense, but retains certain features of criticality, which we term pseudo-critical. Whilst an inability to satisfy a Ginzburg criterion implies that fluctuations remain relevant at macroscopic scales, finite-wavenumber fluctuations grow at finite rates and exhibit non-trivial dispersion relations. The interplay between the growth of fluctuations and the speed at which they move relative to the bulk results in distinct regimes of micro- and meso-phase separation.

cond-mat.stat-mech↗

arXiv2025

A Dean-Kawasaki equation for reaction diffusion systems driven by Poisson noise

We derive a stochastic partial differential equation that describes the fluctuating behaviour of reaction-diffusion systems of N particles, undergoing Markovian, unary reactions. This generalises the work of Dean [J. Phys. A: Math. and Gen., 29 (24), L613, (1996)] through the inclusion of random Poisson fields. Our approach is based on weak interactions, which has the dual benefit that the resulting equations asymptotically converge (in the N to infinity limit) on a variation of a McKean- Vlasov diffusion, whilst still being related to the case of Dean-like strong interactions via a trivial rescaling. Various examples are presented, alongside a discussion of possible extensions to more complicated reaction schemes.

cond-mat.stat-mech↗

arXiv2022

Bivalent Kinetics: Insights from Many Body Physics

Bivalency confers several concentration-dependent phenomena, including avidity, competitive exchange and multi-site competitive exchange. Since these concepts are crucial for a wide variety of topics in cell and molecular biology, their extension, modification and/or re-purposing is also increasingly important for the design and construction of de-novo synthetic systems at the nanoscale. In this context, we draw upon classical techniques of statistical physics to revisit bivalency, highlighting that receptor site geometry offers a design modality independent of the chemistry of the individual binding interfaces themselves. Recasting the problem in terms of many-body coordination, we explore extended, translationally-invariant chains and lattices of receptor sites. This not only brings clarity to behaviours associated with simpler motifs, but also enables us to distil core principles for the rational design of concentration-dependent kinetics in synthetic soft-systems, which centre on the notion of geometric frustration. In doing so, we also reveal the possibility of other tunable spatio-temporal features, such as correlation lengths, mean-squared displacements and percolation-like transitions.

cond-mat.stat-mech↗

arXiv2019

Thermodynamics of emergent structure in active matter

Active matter is rapidly becoming a key paradigm of out-of-equilibrium soft matter exhibiting complex collective phenomena, yet the thermodynamics of such systems remain poorly understood. In this letter we study the nonequilbrium thermodynamics of large scale active systems capable of mobility-induced phase separation and polar alignment, using a fully under-damped model which exhibits hidden entropy productions not previously reported in the literature. We quantify steady state entropy production at each point in the phase diagram, revealing characteristic dissipation rates associated with the distinct phases and configurational structure. This reveals sharp discontinuities in the entropy production at phase transitions and facilitates identification of the thermodynamics of micro-features, such as defects in the emergent structure. The interpretation of the time reversal symmetry in the dynamics of the particles is found to be crucial.

cond-mat.stat-mech↗

arXiv2018

Entropy balance and Information processing in bipartite and non-bipartite composite systems

Information dynamics is an emerging description of information processing in complex systems which describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper we make a formal analogy between information dynamics and stochastic thermodynamics which describes the thermal behaviour of small irreversible systems. As stochastic dynamics is increasingly being utilized to quantify the thermodynamics associated with the processing of information we suggest such an analogy is instructive, highlighting that existing thermodynamic quantities can be described solely in terms of extant information theoretic measures related to information processing. In this contribution we construct irreversibility measures in terms of these quantities and relate them to the physical entropy productions that characterise the behaviour of single and composite systems in stochastic thermodynamics illustrating them with simple examples. Moreover, we can apply such a formalism to systems which do not have a bipartite structure. In particular we demonstrate that, given suitable non-bipartite processes, the heat flow in a subsystem can still be identified and one requires the present formalism to recover generalizations of the second law. In these systems residual irreversibility is associated with neither subsystem and this must be included in the these generalised second laws. This opens up the possibility of describing all physical systems in terms of computation allowing us to propose a framework for discussing the reversibility of systems traditionally out of scope of stochastic thermodynamics.

cond-mat.stat-mech↗

arXiv2018

Information ratchets exploiting spatially structured information reservoirs

Information ratchets extract work from heat baths using low entropy information reservoirs. We find that the structure of the reservoirs affects both their performance and phase diagram. By deriving exact probabilities of recurrence in d-dimensional reservoirs we calculate the net extraction of work. Performance is characterised by two critical dimensions (i) For d < 3 driven exploration of the reservoir is essential to extract work (ii) For d > 4 purely diffusive exploration is optimal. This has important consequences for computation where sequential operations constitute a 1D path.

cond-mat.stat-mech↗

arXiv2018

Characterising information-theoretic storage and transfer in continuous time processes

The characterisation of information processing is an important task in complex systems science. Information dynamics is a quantitative methodology for modelling the intrinsic information processing conducted by a process represented as a time series, but to date has only been formulated in discrete time. Building on previous work which demonstrated how to formulate transfer entropy in continuous time, we give a total account of information processing in this setting, incorporating information storage. We find that a convergent rate of predictive capacity, comprised of the transfer entropy and active information storage, does not exist, arising through divergent rates of active information storage. We identify that active information storage can be decomposed into two separate quantities that characterise predictive capacity stored in a process: active memory utilisation and instantaneous predictive capacity. The latter involves prediction related to path regularity and so solely inherits the divergent properties of the active information storage, whilst the former permits definitions of pathwise and rate quantities. We formulate measures of memory utilisation for jump and neural spiking processes and illustrate measures of information processing in synthetic neural spiking models and coupled Ornstein-Uhlenbeck models. The application to synthetic neural spiking models demonstrates that active memory utilisation for point processes consists of discontinuous jump contributions (at spikes) interrupting a continuously varying contribution (relating to waiting times between spikes), complementing the behaviour previously demonstrated for transfer entropy in these processes.

cs.IT↗

arXiv2018

Thermodynamics and computation during collective motion near criticality

We study self-organisation of collective motion as a thermodynamic phenomenon, in the context of the first law of thermodynamics. It is expected that the coherent ordered motion typically self-organises in the presence of changes in the (generalised) internal energy and of (generalised) work done on, or extracted from, the system. We aim to explicitly quantify changes in these two quantities in a system of simulated self-propelled particles, and contrast them with changes in the system's configuration entropy. In doing so, we adapt a thermodynamic formulation of the curvatures of the internal energy and the work, with respect to two parameters that control the particles' alignment. This allows us to systematically investigate the behaviour of the system by varying the two control parameters to drive the system across a kinetic phase transition. Our results identify critical regimes and show that during the phase transition, where the configuration entropy of the system decreases, the rates of change of the work and of the internal energy also decrease, while their curvatures diverge. Importantly, the reduction of entropy achieved through expenditure of work is shown to peak at criticality. We relate this both to a thermodynamic efficiency and the significance of the increased order with respect to a computational path. Additionally, this study provides an information-geometric interpretation of the curvature of the internal energy as the difference between two curvatures: the curvature of the free entropy, captured by the Fisher information, and the curvature of the configuration entropy.

cond-mat.stat-mech↗

arXiv2017

Transfer entropy in continuous time, with applications to jump and neural spiking processes

Transfer entropy has been used to quantify the directed flow of information between source and target variables in many complex systems. While transfer entropy was originally formulated in discrete time, in this paper we provide a framework for considering transfer entropy in continuous time systems, based on Radon-Nikodym derivatives between measures of complete path realizations. To describe the information dynamics of individual path realizations, we introduce the pathwise transfer entropy, the expectation of which is the transfer entropy accumulated over a finite time interval. We demonstrate that this formalism permits an instantaneous transfer entropy rate. These properties are analogous to the behavior of physical quantities defined along paths such as work and heat. We use this approach to produce an explicit form for the transfer entropy for pure jump processes, and highlight the simplified form in the specific case of point processes (frequently used in neuroscience to model neural spike trains). Finally, we present two synthetic spiking neuron model examples to exhibit the pertinent features of our formalism, namely, that the information flow for point processes consists of discontinuous jump contributions (at spikes in the target) interrupting a continuously varying contribution (relating to waiting times between target spikes). Numerical schemes based on our formalism promise significant benefits over existing strategies based on discrete time formalisms.

cs.IT↗

arXiv2012

Entropy production from stochastic dynamics in discrete full phase space

The stochastic entropy generated during the evolution of a system interacting with an environment may be separated into three components, but only two of these have a non-negative mean. The third component of entropy production is associated with the relaxation of the system probability distribution towards a stationary state and with nonequilibrium constraints within the dynamics that break detailed balance. It exists when at least some of the coordinates of the system phase space change sign under time reversal, and when the stationary state is asymmetric in these coordinates. We illustrate the various components of entropy production, both in detail for particular trajectories and in the mean, using simple systems defined on a discrete phase space of spatial and velocity coordinates. These models capture features of the drift and diffusion of a particle in a physical system, including the processes of injection and removal and the effect of a temperature gradient. The examples demonstrate how entropy production in stochastic thermodynamics depends on the detail that is included in a model of the dynamics of a process. Entropy production from such a perspective is a measure of the failure of such models to meet Loschmidt's expectation of dynamic reversibility.

cond-mat.stat-mech↗

arXiv2012

Entropy production in full phase space for continuous stochastic dynamics

The total entropy production and its three constituent components are described both as fluctuating trajectory-dependent quantities and as averaged contributions in the context of the continuous Markovian dynamics, described by stochastic differential equations with multiplicative noise, of systems with both odd and even coordinates with respect to time reversal, such as dynamics in full phase space. Two of these constituent quantities obey integral fluctuation theorems and are thus rigorously positive in the mean by Jensen's inequality. The third, however, is not and furthermore cannot be uniquely associated with irreversibility arising from relaxation, nor with the breakage of detailed balance brought about by non-equilibrium constraints. The properties of the various contributions to total entropy production are explored through the consideration of two examples: steady state heat conduction due to a temperature gradient, and transitions between stationary states of drift-diffusion on a ring, both in the context of the full phase space dynamics of a single Brownian particle.

cond-mat.stat-mech↗

arXiv2012

Non-equilibrium thermodynamics of stochastic systems with odd and even variables

The total entropy production of stochastic systems can be divided into three quantities. The first corresponds to the excess heat, whilst the second two comprise the house-keeping heat. We denote these two components the transient and generalised house-keeping heat and we obtain an integral fluctuation theorem for the latter, valid for all Markovian stochastic dynamics. A previously reported formalism is obtained when the stationary probability distribution is symmetric for all variables that are odd under time reversal which restricts consideration of directional variables such as velocity.

cond-mat.stat-mech↗

arXiv2012

Fluctuation relations: a pedagogical overview

The fluctuation relations have received considerable attention since their emergence and development in the 1990s. We present a summary of the main results and suggest ways to interpret this material. Starting with a consideration of the under-determined time evolution of a simple open system, formulated using continuous Markovian stochastic dy- namics, an expression for the entropy generated over a time interval is developed in terms of the probability of observing a trajectory associated with a prescribed driving protocol, and the probability of its time-reverse. This forms the basis for a general theoretical description of non-equilibrium thermodynamic pro- cesses. Having established a connection between entropy production and an inequivalence in probability for forward and time-reversed events, we proceed in the manner of Sekimoto and Seifert, in particular, to derive results in stochastic thermodynamics: a description of the evolution of a system between equilibrium states that ties in with well-established thermodynamic expectations. We derive fluctuation relations, state conditions for their validity, and illustrate their op- eration in some simple cases, thereby providing some introductory insight into the various celebrated symmetry relations that have emerged in this field.

cond-mat.stat-mech↗