arXiv subjects

Christopher Jarzynski

Publications and source records attributed to Christopher Jarzynski.

At least 37 records · Page 2Linked to original sources

arXiv2021

Understanding cytoskeletal avalanches using mechanical stability analysis

Eukaryotic cells are mechanically supported by a polymer network called the cytoskeleton, which consumes chemical energy to dynamically remodel its structure. Recent experiments in vivo have revealed that this remodeling occasionally happens through anomalously large displacements, reminiscent of earthquakes or avalanches. These cytoskeletal avalanches might indicate that the cytoskeleton's structural response to a changing cellular environment is highly sensitive, and they are therefore of significant biological interest. However, the physics underlying "cytoquakes" is poorly understood. Here, we use agent-based simulations of cytoskeletal self-organization to study fluctuations in the network's mechanical energy. We robustly observe non-Gaussian statistics and asymmetrically large rates of energy release compared to accumulation in a minimal cytoskeletal model. The large events of energy release are found to correlate with large, collective displacements of the cytoskeletal filaments. We also find that the changes in the localization of tension and the projections of the network motion onto the vibrational normal modes are asymmetrically distributed for energy release and accumulation. These results imply an avalanche-like process of slow energy storage punctuated by fast, large events of energy release involving a collective network rearrangement. We further show that mechanical instability precedes cytoquake occurrence through a machine learning model that dynamically forecasts cytoquakes using the vibrational spectrum as input. Our results provide the first connection between the cytoquake phenomenon and the network's mechanical energy and can help guide future investigations of the cytoskeleton's structural susceptibility.

physics.bio-ph↗

arXiv2021

Energy diffusion and absorption in chaotic systems with rapid periodic driving

When a chaotic, ergodic Hamiltonian system with $N$ degrees of freedom is subject to sufficiently rapid periodic driving, its energy evolves diffusively. We derive a Fokker-Planck equation that governs the evolution of the system's probability distribution in energy space, and we provide explicit expressions for the energy drift and diffusion rates. Our analysis suggests that the system generically relaxes to a long-lived "prethermal" state characterized by minimal energy absorption, eventually followed by more rapid heating. When $N\gg 1$, the system ultimately absorbs energy indefinitely from the drive, or at least until an infinite temperature state is reached.

cond-mat.stat-mech↗

arXiv2021

Semiclassical fast-forward shortcuts to adiabaticity

In fast forward quantum shortcuts to adiabaticity, a designed potential $U_{FF}(q,t)$ steers a wavefunction to evolve from the $n$'th eigenstate of an initial Hamiltonian $\hat H(0)$ to the $n$'th eigenstate of a final Hamiltonian $\hat H(τ)$, in finite time $τ$. Previously proposed strategies for constructing $U_{FF}$ are (in the absence of special symmetries) limited to the ground state, $n=0$. We develop a method that overcomes this limitation, thereby substantially expanding the applicability of this shortcut to adiabaticity, and we illustrate its effectiveness with numerical simulations. Semiclassical analysis provides insight and establishes a close correspondence with the analogous classical fast forward method.

quant-ph↗

arXiv2019

Machine learning the thermodynamic arrow of time

The mechanism by which thermodynamics sets the direction of time's arrow has long fascinated scientists. Here, we show that a machine learning algorithm can learn to discern the direction of time's arrow when provided with a system's microscopic trajectory as input. The performance of our algorithm matches fundamental bounds predicted by nonequilibrium statistical mechanics. Examination of the algorithm's decision-making process reveals that it discovers the underlying thermodynamic mechanism and the relevant physical observables. Our results indicate that machine learning techniques can be used to study systems out of equilibrium, and ultimately to uncover physical principles.

cond-mat.stat-mech↗

arXiv2019

Fluctuation relations and strong inequalities for thermally isolated systems

For processes during which a macroscopic system exchanges no heat with its surroundings, the second law of thermodynamics places two lower bounds on the amount of work performed on the system: a weak bound, expressed in terms of a fixed-temperature free energy difference, $W \ge ΔF_T$ , and a strong bound, given by a fixed-entropy internal energy difference, $W \ge ΔE_S$ . It is known that statistical inequalities related to the weak bound can be obtained from the nonequilibrium work relation, $\langle\exp (-βW)\rangle = \exp(-βΔF_T)$ . Here we derive an integral fluctuation relation $\langle\exp(-βX) \rangle = 1 $ that is constructed specifically for adiabatic processes, and we use this result to obtain inequalities related to the strong bound, $W \ge ΔE_S$ . We provide both classical and quantum derivations of these results.

cond-mat.stat-mech↗

arXiv2019

Quantifying Dissipation in Actomyosin Networks

Quantifying entropy production in various active matter phases will open new avenues for probing self-organization principles in these far-from-equilibrium systems. It has been hypothesized that the dissipation of free energy by active matter systems may be optimized to produce highly dissipative dynamical states, hence, leading to spontaneous emergence of more ordered states. This interesting idea has not been widely tested. In particular, it is not clear whether emergent states of actomyosin networks, which represent a salient example of biological active matter, self-organize following the principle of dissipation optimization. In order to start addressing this question using detailed computational modeling, we rely on the MEDYAN simulation platform, which allows simulating active matter networks from fundamental molecular principles. We have extended the capabilities of MEDYAN to allow quantification of the rates of dissipation resulting from chemical reactions and relaxation of mechanical stresses during simulation trajectories. We validate our approach with a mean-field model that estimates the rates of dissipation from filament treadmilling. Applying this methodology to the self-organization of small disordered actomyosin networks, we find that compact and highly cross-linked networks tend to allow more efficient transduction of chemical free energy into mechanical energy. In these simple systems, we do not observe that spontaneous network reorganizations lead to increases in the total dissipation rate as predicted by the dissipation-driven adaptation hypothesis mentioned above. However, whether such a principle operates in more general, more complex cytoskeletal networks remains to be investigated.

physics.bio-ph↗

arXiv2019

Optimal probabilistic work extraction beyond the free energy difference with a single-electron device

We experimentally realize protocols that allow to extract work beyond the free energy difference from a single electron transistor at the single thermodynamic trajectory level. With two carefully designed out-of-equilibrium driving cycles featuring kicks of the control parameter, we demonstrate work extraction up to large fractions of $k_BT$ or with probabilities substantially greater than 1/2, despite zero free energy difference over the cycle. Our results are explained in the framework of nonequilibrium fluctuation relations. We thus show that irreversibility can be used as a resource for optimal work extraction even in the absence of feedback from an external operator.

cond-mat.stat-mech↗

arXiv2019

A Discrete Approximation to Gibbs Free Energy of Chemical Reactions is Needed for Accurately Calculating Entropy Production in Mesoscopic Simulations

In modeling the interior of cells by simulating a reaction-diffusion master equation over a grid of compartments, one employs the assumption that the copy numbers of various chemical species are small, discrete quantities. We show that in this case, textbook expressions for the change in Gibbs free energy accompanying a chemical reaction or diffusion between adjacent compartments become inaccurate. We derive exact expressions for these free energy changes under the assumption of discrete copy numbers and illustrate how these expressions reduce to the textbook expressions under a series of successive approximations leveraging the relative sizes of the stoichiometric coefficients and the copy numbers of the solutes and solvent. Numerical results are presented to corroborate the claim that if the copy numbers are treated as discrete quantities, then only these more exact expressions lead to correct equilibrium behavior. The newly derived expressions are critical for correctly tracking dissipation and entropy production in mesoscopic simulations based on the reaction-diffusion master equation formalism.

physics.chem-ph↗

arXiv2018

Similarities and Differences Between Nonequilibrium Steady States and Time-Periodic Driving in Diffusive Systems

A system that violates detailed balance evolves asymptotically into a nonequilibrium steady state with non-vanishing currents. Analogously, when detailed balance holds at any instant of time but the system is driven through time-periodic variations of external parameters, it evolves toward a time-periodic state, which can also support non-vanishing currents. In both cases the maintenance of currents throughout the system incurs a cost in terms of entropy production. Here we compare these two scenarios for one dimensional diffusive systems with periodic boundary condition, a framework commonly used to model biological and artificial molecular machines. We first show that the entropy production rate in a periodically driven system is necessarily greater than that in a stationary system without detailed balance, when both are described by the same (time-averaged) current and probability distribution. Next, we show how to construct both a non-equilibrium steady state and a periodic driving that support a given time averaged probability distribution and current. Lastly, we show that although the entropy production rate of a periodically driven system is higher than that of an equivalent steady state, the difference between the two entropy production rates can be tuned to be arbitrarily small.

cond-mat.stat-mech↗

arXiv2018

Non-conservative Forces via Quantum Reservoir Engineering

A systematic approach is given for engineering dissipative environments that steer quantum wavepackets along desired trajectories. The methodology is demonstrated with several illustrative examples: environment-assisted tunneling, trapping, effective mass assignment, and pseudo-relativistic behavior. Non-conservative stochastic forces do not inevitably lead to decoherence - we show that purity can be well-preserved. These findings highlight the flexibility offered by non-equilibrium open quantum dynamics.

quant-ph↗

arXiv2017

Experimental realization of Feynman's ratchet

Feynman's ratchet is a microscopic machine in contact with two heat reservoirs, at temperatures $T_A$ and $T_B$, that was proposed by Richard Feynman to illustrate the second law of thermodynamics. In equilibrium ($T_A=T_B$), thermal fluctuations prevent the ratchet from generating directed motion. When the ratchet is maintained away from equilibrium by a temperature difference ($T_A \ne T_B$), it can operate as a heat engine, rectifying thermal fluctuations to perform work. While it has attracted much interest, the operation of Feynman's ratchet as a heat engine has not been realized experimentally, due to technical challenges. In this work, we realize Feynman's ratchet with a colloidal particle in a one dimensional optical trap in contact with two heat reservoirs: one is the surrounding water, while the effect of the other reservoir is generated by a novel feedback mechanism, using the Metropolis algorithm to impose detailed balance. We verify that the system does not produce work when $T_A=T_B$, and that it becomes a microscopic heat engine when $T_A \ne T_B$. We analyze work, heat and entropy production as functions of the temperature difference and external load. Our experimental realization of Feynman's ratchet and the Metropolis algorithm can also be used to study the thermodynamics of feedback control and information processing, the working mechanism of molecular motors, and controllable particle transportation.

cond-mat.stat-mech↗

arXiv2017

Shortcuts to adiabaticity using flow fields

A $\textit{shortcut to adiabaticity}$ is a recipe for generating adiabatic evolution at an arbitrary pace. Shortcuts have been developed for quantum, classical and (most recently) stochastic dynamics. A shortcut might involve a $\textit{counterdiabatic}$ Hamiltonian that causes a system to follow the adiabatic evolution at all times, or it might utilize a $\textit{fast-forward}$ potential, which returns the system to the adiabatic path at the end of the process. We develop a general framework for constructing shortcuts to adiabaticity from $\textit{flow fields}$ that describe the desired adiabatic evolution. Our approach encompasses quantum, classical and stochastic dynamics, and provides surprisingly compact expressions for both counterdiabatic Hamiltonians and fast-forward potentials. We illustrate our method with numerical simulations of a model system, and we compare our shortcuts with previously obtained results. We also consider the semiclassical connections between our quantum and classical shortcuts. Our method, like the fast-forward approach developed by previous authors, is susceptible to singularities when applied to excited states of quantum systems; we propose a simple, intuitive criterion for determining whether these singularities will arise, for a given excited state.

quant-ph↗

arXiv2017

Low-Dimensional Manifold of Actin Polymerization Dynamics

Actin filaments are critical components of the eukaryotic cytoskeleton, playing important roles in a number of cellular functions, such as cell migration, organelle transport, and mechanosensation. They are helical polymers with a well-defined polarity, composed of globular monomers that bind nucleotides in one of three hydrolysis states (ATP, ADP-Pi, or ADP). Mean-field models of the dynamics of actin polymerization have succeeded in, among other things, determining the nucleotide profile of an average filament and resolving the mechanisms of accessory proteins, however these models require numerical solution of a high-dimensional system of nonlinear ODE's. By truncating a set of recursion equations, the Brooks-Carlsson model reduces dimensionality to 11, but it remains nonlinear and does not admit an analytical solution, hence, significantly hindering understanding of its resulting dynamics. In this work, by taking advantage of the fast timescales of the hydrolysis states of the filament tips, we propose two model reduction schemes that achieve low dimensionality and linearity. We provide an exact solution of the resulting linear equations and use it to shed light on the dynamical behaviors of the full BC model, highlighting the relative ordering of the timescales of various collective processes, and explaining some unusual dependence of the steady-state behavior on initial conditions.

q-bio.SC↗

arXiv2017

Verification of the Quantum Nonequilibrium Work Relation in the Presence of Decoherence

Although nonequilibrium work and fluctuation relations have been studied in detail within classical statistical physics, extending these results to open quantum systems has proven to be conceptually difficult. For systems that undergo decoherence but not dissipation, we argue that it is natural to define quantum work exactly as for isolated quantum systems, using the two-point measurement protocol. Complementing previous theoretical analysis using quantum channels, we show that the nonequilibrium work relation remains valid in this situation, and we test this assertion experimentally using a system engineered from an optically trapped ion. Our experimental results reveal the work relation's validity over a variety of driving speeds, decoherence rates, and effective temperatures and represent the first confirmation of the work relation for non-unitary dynamics.

cond-mat.stat-mech↗

arXiv2016

Heat dissipation and fluctuations in a driven quantum dot

While thermodynamics is a useful tool to describe the driving of large systems close to equilibrium, fluctuations dominate the distribution of heat and work in small systems and far from equilibrium. We study the heat generated by driving a small system and change the drive parameters to analyse the transition from a drive leaving the system close to equilibrium to driving it far from equilibrium. Our system is a quantum dot in a GaAs/AlGaAs heterostructure hosting a two-dimensional electron gas. The dot is tunnel-coupled to one part of the two-dimensional electron gas acting as a heat and particle reservoir. We use standard rate equations to model the driven dot-reservoir system and find excellent agreement with the experiment. Additionally, we quantify the fluctuations by experimentally test the theoretical concept of the arrow of time, predicting our ability to distinguish whether a process goes in the forward or backward drive direction.

cond-mat.mes-hall↗

arXiv2016

Fast forward to the classical adiabatic invariant

We show how the classical action, an adiabatic invariant, can be preserved under non-adiabatic conditions. Specifically, for a time-dependent Hamiltonian $H = p^2/2m + U(q,t)$ in one degree of freedom, and for an arbitrary choice of action $I_0$, we construct a "fast-forward" potential energy function $V_{\rm FF}(q,t)$ that, when added to $H$, guides all trajectories with initial action $I_0$ to end with the same value of action. We use this result to construct a local dynamical invariant $J(q,p,t)$ whose value remains constant along these trajectories. We illustrate our results with numerical simulations. Finally, we sketch how our classical results may be used to design approximate quantum shortcuts to adiabaticity.

physics.class-ph↗

arXiv2016

Classical and quantum shortcuts to adiabaticity in a tilted piston

Adiabatic quantum state evolution can be accelerated through a variety of shortcuts to adiabaticity. In one approach, a counterdiabatic quantum Hamiltonian $\hat H_{CD}$ is constructed to suppress nonadiabatic excitations. In the analogous classical problem, a counterdiabatic classical Hamiltonian $H_{CD}$ ensures that the classical action remains constant even under rapid driving. Both the quantum and classical versions of this problem have been solved for the special case of scale-invariant driving, characterized by linear expansions, contractions or translations of the system. Here we investigate an example of a non-scale-invariant system -- a tilted piston. We solve exactly for the classical counterdiabatic Hamiltonian $H_{CD}(q,p,t)$, which we then quantize to obtain a Hermitian operator $\hat H_{CD}(t)$. Using numerical simulations, we find that $\hat H_{CD}$ effectively suppresses non-adiabatic excitations under rapid driving. These results offer a proof of principle -- beyond the special case of scale-invariant driving -- that quantum shortcuts to adiabaticity can successfully be constructed from their classical counterparts.

quant-ph↗

arXiv2016

Number of trials required to estimate a free-energy difference, using fluctuation relations

The difference Delta F between free energies has applications in biology, chemistry, and pharmacology. The value of Delta F can be estimated from experiments or simulations, via fluctuation theorems developed in statistical mechanics. Calculating the error in a Delta F estimate is difficult. Worse, atypical trials dominate estimates. How many trials one should perform was estimated roughly in [Jarzynski, Phys. Rev. E 73, 046105 (2006)]. We enhance the approximation with information-theoretic strategies: We quantify "dominance" with a tolerance parameter chosen by the experimenter or simulator. We bound the number of trials one should expect to perform, using the order-infinity Renyi entropy. The bound can be estimated if one implements the "good practice" of bidirectionality, known to improve estimates of Delta F. Estimating Delta F from this number of trials leads to an error that we bound approximately. Numerical experiments on a weakly interacting dilute classical gas support our analytical calculations.

cond-mat.stat-mech↗