arXiv subjects

Ian J. Ford

Publications and source records attributed to Ian J. Ford.

At least 19 recordsLinked to original sources

arXiv2025

Measurement dependence in a Bell inequality arising from the dynamics of hidden variables

Bell inequalities rely on an assumption that the probabilities of adopting configurations of hidden variables describing a system prior to measurement are independent of the choice of measured physical property, also known as measurement independence. Weakening this assumption could alter the inequalities to accommodate experimental data whilst maintaining local interactions. A natural avenue for achieving this would be to model measurement as a dynamical process involving an interaction between the system and its environment (the measurement apparatus), that drives the hidden variables towards attractors representing measurement outcomes of the observable. Implementing such hidden variable dynamics, we can infer from observed correlations the hidden variable probability distributions before measurement, which differ according to which measurement settings were chosen. We explore various models of the dynamics of the hidden variables under measurement, revealing features that can create measurement dependence and others that can not.

quant-ph↗

arXiv2025

Characterising quantum measurement through environmental stochastic entropy production in a two spin 1/2 system

Quantum state diffusion is a framework within which measurement may be described as the continuous and gradual collapse of a quantum system to an eigenstate as a result of interaction with its environment. The irreversible nature of the quantum trajectories that arise may be characterised by the environmental stochastic entropy production associated with the measurement. We consider a system of two spin 1/2 particles undergoing either single particle measurements or measurements of the total z-spin component S_{z}. The mean asymptotic rates of environmental stochastic entropy production associated with collapse can depend on the eigenstate of S_{z} selected, and on the initial state of the system, offering an additional avenue for characterising quantum measurement.

quant-ph↗

arXiv2024

Stochastic entropy production associated with quantum measurement in a framework of Markovian quantum state diffusion

The reduced density matrix that characterises the state of an open quantum system is a projection from the full density matrix of the quantum system and its environment, and there are many full density matrices consistent with a given reduced version. Without a specification of relevant details of the environment, the evolution of a reduced density matrix is therefore typically unpredictable, even if the dynamics are deterministic. With this in mind, we investigate a two level open quantum system using a framework of quantum state diffusion. We consider the pseudorandom evolution of its reduced density matrix when subjected to an environment-driven process of continuous quantum measurement of a system observable, using dynamics that asymptotically send the system to an eigenstate. The unpredictability is characterised by a stochastic entropy production, the average of which corresponds to an increase in the subjective uncertainty of the quantum state adopted by the system and environment, given the underspecified dynamics. This differs from a change in von Neumann entropy, and can continue indefinitely as the system is guided towards an eigenstate. As one would expect, the simultaneous measurement of two non-commuting observables within the same framework does not send the system to an eigenstate. Instead, the probability density function describing the reduced density matrix of the system becomes stationary over a continuum of pure states, a situation characterised by zero further stochastic entropy production. Transitions between such stationary states, brought about by changes in the relative strengths of the two measurement processes, give rise to finite positive mean stochastic entropy production. The framework investigated can offer useful perspectives on both the dynamics and irreversible thermodynamics of measurement in quantum systems.

quant-ph↗

arXiv2024

Memory effects in a sequence of measurements of non-commuting observables

We use continuous, stochastic quantum trajectories within a framework of quantum state diffusion (QSD) to describe alternating measurements of two non-commuting observables. Projective measurement of an observable completely destroys memory of the outcome of a previous measurement of the conjugate observable. In contrast, measurement under QSD is not projective and it is possible to vary the rate at which information about previous measurement outcomes is lost by changing the strength of measurement. We apply our methods to a spin 1/2 system and a spin 1 system undergoing alternating measurements of the $S_{z}$ and $S_{x}$ spin observables. Performing strong $S_{z}$ measurements and weak $S_{x}$ measurements on the spin 1 system, we demonstrate return to the same eigenstate of $S_{z}$ to a degree beyond that expected from projective measurements and the Born rule. Such a memory effect appears to be greater for return to the $\pm1$ eigenstates than the $0$ eigenstate. Furthermore, the spin 1 system follows a measurement cascade process where an initial superposition of the three eigenstates of the observable evolves into a superposition of just two, before finally collapsing into a single eigenstate, giving rise to a distinctive pattern of evolution of the spin components.

quant-ph↗

arXiv2024

Stochastic quantum trajectories demonstrate the Quantum Zeno Effect in open spin 1/2, spin 1 and spin 3/2 systems

We investigate the Quantum Zeno Effect in spin 1/2, spin 1 and spin 3/2 open quantum systems undergoing Rabi oscillations, revealing unexplored features for the spin 1 and spin 3/2 systems. The systems interact with an environment designed to perform continuous measurements of an observable, driving the systems stochastically towards one of the eigenstates of the corresponding operator. The system-environment coupling constant represents the strength of the measurement. Stochastic quantum trajectories are generated by unravelling a Markovian Lindblad master equation using the quantum state diffusion formalism. These are regarded as a more appropriate representation of system behaviour than consideration of the averaged evolution since the latter can mask the effect of measurement. Complete positivity is maintained and thus the trajectories can be considered as physically meaningful. The Quantum Zeno Effect is investigated over a range of measurement strengths. Increasing the strength leads to greater system dwell in the vicinity of the eigenstates of the measured observable and lengthens the time taken by the system to return to that eigenstate,thus the Quantum Zeno Effect emerges. For very strong measurement, the Rabi oscillations resemble randomly occurring near-instantaneous jumps between eigenstates. The trajectories followed by the quantum system are heavily dependent on the measurement strength which other than slowing down and adding noise to the Rabi oscillations, changes the paths taken in spin phase space from a circular precession into elaborate figures-of-eight. For spin 1 and spin 3/2 systems, the measurement strength determines which eigenstates are explored and the Quantum Zeno Effect is stronger when the system dwells in the vicinity of certain eigenstates compared to others.

quant-ph↗

arXiv2023

Three components of stochastic entropy production associated with the quantum Zeno and anti-Zeno effects

We investigate stochastic entropy production in a two-level quantum system that performs Rabi oscillations while undergoing quantum measurement brought about by continuous random disturbance by an external measuring device or environment. The dynamics produce quantum Zeno and anti-Zeno effects for certain measurement regimes, and the stochastic entropy production is a measure of the irreversibility of the behaviour. When the strength of the measurement disturbance is time-dependent, the stochastic entropy production separates into three components. Two represent relaxational behaviour, one being specific to systems represented by coordinates that are odd under time reversal symmetry, and a third characterises the nonequilibrium stationary state arising from breakage of detailed balance in the dynamics. The study illustrates how the ideas of stochastic thermodynamics may be applied in similar ways to both quantum and classical systems.

quant-ph↗

arXiv2023

Apparent pathologies in stochastic entropy production in the thermalisation of an open two-level quantum system

We investigate the entropic consequences of the relaxation of an open two-level quantum system towards a thermalised statistical state, using a framework of quantum state diffusion with a minimal set of raising and lowering Lindblad operators. We demonstrate that thermalisation starting from a general state is accompanied by a persistent non-zero mean rate of change of the environmental component of stochastic entropy production. This thermodynamic signature can be associated with the purification of the reduced density matrix $ρ$ of the randomly evolving state, to be contrasted with the impurity of the more often considered ensemble average of $ρ$. The system adopts stationary statistics, with zero stochastic entropy production, once purity has been achieved. However, we show that apparent pathological mathematical difficulties in the computation of stochastic entropy production emerge if $ρ$ is represented using a certain set of coordinates, though these can be removed by choosing a different set. We conclude that frameworks for modelling open quantum systems must be carefully selected to provide satisfactory thermodynamic as well as dynamic behaviour.

quant-ph↗

arXiv2023

Stochastic entropy production for dynamical systems with restricted diffusion

Modelling the evolution of a system using stochastic dynamics typically implies a greater subjective uncertainty in the adopted system coordinates as time progresses, and stochastic entropy production has been developed as a measure of this change. In some situations the evolution of stochastic entropy production can be described using an Itô process, but mathematical difficulties can emerge if diffusion in the system phase space is restricted to a subspace of lower dimension. This can arise if there are constants of the motion, for example, or more generally when there are functions of the coordinates that evolve without noise. We discuss such a case for an open three-level quantum system modelled within a framework of Markovian quantum state diffusion and show how the problem of computing the stochastic entropy production in such a situation can be overcome. We go on to illustrate how a nonequilibrium stationary state of the three-level system, with a constant mean production rate of stochastic entropy, can be established under suitable environmental couplings.

cond-mat.stat-mech↗

arXiv2022

Positively Charged Additives Facilitate Incorporation in Inorganic Single Crystals

Incorporation of guest additives within inorganic single crystals offers a unique strategy for creating nanocomposites with tailored properties. While anionic additives have been widely used to control the properties of crystals, their effective incorporation remains a key challenge. Here, we show that cationic additives are an excellent alterative for the synthesis of nanocomposites, where they are shown to deliver exceptional levels of incorporation of up to 70 wt% of positively charged amino acids, polymer particles, gold nanoparticles, and silver nanoclusters within inorganic single crystals. This high additive loading endows the nanocomposites with new functional properties including plasmon coupling, bright fluorescence, and surface-enhanced Raman scattering (SERS). Cationic additives are also shown to outperform their acidic counterparts, where they are highly active in a wider range of crystal systems, owing to their outstanding colloidal stability in the crystallization media and strong affinity for the crystal surfaces. This work demonstrates that although often overlooked, cationic additives can make valuable crystallization additives to create composite materials with tailored composition-structure-property relationships. This versatile and straightforward approach advances the field of single-crystal composites and provides exciting prospects for the design and fabrication of new hybrid materials with tunable functional properties.

cond-mat.mtrl-sci↗

arXiv2018

Dissipation production in a closed two-level quantum system as a test of the obversibility of the dynamics

Irreversible behaviour is traditionally associated with open stochastic dynamical systems, but an asymmetry in the probabilistic specification of a closed deterministic system can similarly lead to a disparity between the likelihoods of a particular forward and corresponding backward behaviour starting from a specified time. Such a comparison is a test of a property denoted obversibility, which may be quantified in terms of dissipation production as a measure of irreversibility. We here discuss the procedure needed to evaluate dissipation production in a simple, deterministic two-level quantum system described by a statistical ensemble of state vectors and then provide numerical results for illustrative situations. We consider cases that both do and do not fulfill an Evans-Searles Fluctuation Theorem for the dissipation production, and identify conditions for which the system will display time-asymmetric average behaviour as it evolves.

quant-ph↗

arXiv2017

Thermogravitational cycles: theoretical framework and example of an electric thermogravitational generator based on balloon inflation/deflation

Several studies have combined heat and gravitational energy exchanges to create novel heat engines. A common theoretical framework is developed here to describe thermogravitational cycles which have the same efficiencies as the Carnot, Rankine or Brayton cycles. Considering a working fluid, enclosed in a balloon, inside a column filled with a transporting fluid, the cycle is composed of four steps. Starting from the top of the column, the balloon goes down by gravity, receives heat from a hot source at the bottom, rises and delivers heat to a cold source at the top. Unlike classic power cycles which need external work to operate the compressor, thermogravitational cycles can operate as "pure power cycle" where no external work is provided to drive the cycle. To illustrate this concept, the prototype of a thermogravitational electrical generator is presented. It uses a hot source of low temperature (average temperature near 57°C) and relies on the gravitational energy exchanges of an organic fluorinated fluid inside a balloon attached to a magnetic marble producing an electromotive force of 50 mV peak to peak by the use of a linear alternator. This heat engine is well suited to be operated using renewable energy sources such as geothermal gradients or focused sunbeams.

physics.gen-ph↗

arXiv2016

Free energy of formation of clusters of sulphuric acid and water molecules determined by guided disassembly

We evaluate the grand potential of a cluster of two molecular species, equivalent to its free energy of formation from a binary vapour phase, using a nonequilibrium molecular dynamics technique where guide particles, each tethered to a molecule by a harmonic force, move apart to disassemble a cluster into its components. The mechanical work performed in an ensemble of trajectories is analysed using the Jarzynski equality to obtain a free energy of disassembly, a contribution to the cluster grand potential. We study clusters of sulphuric acid and water at 300 K, using a classical interaction scheme, and contrast two modes of guided disassembly. In one, the cluster is broken apart through simple pulling by the guide particles, but we find the trajectories tend to be mechanically irreversible. In the second approach, the guide motion and strength of tethering are modified in a way that prises the cluster apart, a procedure that seems more reversible. We construct a surface representing the cluster grand potential, and identify a critical cluster for droplet nucleation under given vapour conditions. We compare the equilibrium populations of clusters with calculations reported by Henschel et al. [J. Phys. Chem. A 118, 2599 (2014)] based on optimised quantum chemical structures.

cond-mat.stat-mech↗

arXiv2016

Entropy-reducing dynamics of a double demon

We study the reduction in total entropy, and associated conversion of environmental heat into work, arising from the coupling and decoupling of two systems followed by processing determined by suitable mutual feedback. The scheme is based on the actions of Maxwell's demon, namely the performance of a measurement on a system followed by an exploitation of the outcome to extract work. When this is carried out in a symmetric fashion, with each system informing the exploitation of the other (and both therefore acting as a demon), it may be shown that the second law can be broken, a consequence of the self-sorting character of the system dynamics.

cond-mat.stat-mech↗

arXiv2016

A classical reactive potential for molecular clusters of sulphuric acid and water

We present a two-state empirical valence bond (EVB) potential describing interactions between sulphuric acid and water molecules and designed to model proton transfer between them within a classical dynamical framework. The potential has been developed in order to study the properties of molecular clusters of these species, which are thought to be relevant to atmospheric aerosol nucleation. The particle swarm optimisation method has been used to fit the parameters of the EVB model to density functional theory (DFT) calculations. Features of the parametrised model and DFT data are compared and found to be in satisfactory agreement. In particular, it is found that a single sulphuric acid molecule will donate a proton when clustered with four water molecules at 300 K and that this threshold is temperature dependent.

physics.chem-ph↗

arXiv2015

Maxwell's demon and the management of ignorance in stochastic thermodynamics

It is nearly 150 years since Maxwell challenged the validity of the second law of thermodynamics by imagining a tiny creature who could sort the molecules of a gas in such a way that would decrease entropy without exerting any work. The demon has been discussed largely using thought experiments, but it has recently become possible to exert control over nanoscale systems, just as Maxwell imagined, and the status of the second law has become a more practical matter, raising the issue of how measurements manage our ignorance in a way that can be exploited. The framework of stochastic thermodynamics extends macroscopic concepts such as heat, work, entropy and irreversibility to small systems and allows us explore the matter. Some arguments against a successful demon imply a second law that can be suspended indefinitely until we dissipate energy in order to remove the records of his operations. In contrast, under stochastic thermodynamics the demon fails because on average more work is performed upfront in making a measurement than is to be extracted by exploiting the outcome. This requires us to exclude systems and a demon that evolve under what might be termed self-sorting dynamics, and we reflect on the constraints on control that this implies while still working within a thermodynamic framework.

cond-mat.stat-mech↗

arXiv2015

Maximum entropy principle for stationary states underpinned by stochastic thermodynamics

The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of incomplete information. But such a framework can be more compelling if it is underpinned by dynamical arguments, and we show how this can be provided by stochastic thermodynamics, where an explicit link is made between the production of entropy and the stochastic dynamics of a system coupled to an environment. The separation of entropy production into three components allows us to select a stationary state by maximising the change, averaged over all realisations of the motion, in the principal relaxational or nonadiabatic component, equivalent to requiring that this contribution to the entropy production should become time independent for all realisations. We show that this recovers the usual equilibrium probability density function (pdf) for a conservative system in an isothermal environment, as well as the stationary nonequilibrium pdf for a particle confined to a potential under nonisothermal conditions, and a particle subject to a constant nonconservative force under isothermal conditions. The two remaining components of entropy production account for a recently discussed thermodynamic anomaly between over- and underdamped treatments of the dynamics in the nonisothermal stationary state.

cond-mat.stat-mech↗

arXiv2015

Stochastic entropy production arising from nonstationary thermal transport

We compute statistical properties of the stochastic entropy production associated with the nonstationary transport of heat through a system coupled to a time dependent nonisothermal heat bath. We study the 1-d stochastic evolution of a bound particle in such an environment by solving the appropriate Langevin equation numerically, and by using an approximate analytic solution to the Kramers equation to determine the behaviour of an ensemble of systems. We express the total stochastic entropy production in terms of a relaxational or nonadiabatic part together with two components of housekeeping entropy production and determine the distributions for each, demonstrating the importance of all three contributions for this system. We compare the results with an approximate analytic model of the mean behaviour and we further demonstrate that the total entropy production and the relaxational component approximately satisfy detailed fluctuation relations for certain time intervals. Finally, we comment on the resemblance between the procedure for solving the Kramers equation and a constrained extremisation, with respect to the probability density function, of the spatial density of the mean rate of production of stochastic entropy.

cond-mat.stat-mech↗

arXiv2015

Work relations for a system governed by Tsallis statistics

We derive analogues of the Jarzynski equality and Crooks relation to characterise the nonequilibrium work associated with changes in the spring constant of an overdamped oscillator in a quadratically varying spatial temperature profile. The stationary state of such an oscillator is described by Tsallis statistics, and the work relations for certain processes may be expressed in terms of q-exponentials. We suggest that these identities might be a feature of nonequilibrium processes in circumstances where Tsallis distributions are found.

cond-mat.stat-mech↗