arXiv subjects

Adrianne Zhong

Publications and source records attributed to Adrianne Zhong.

8 recordsLinked to original sources

arXiv2026

Optimal active engines obey the thermodynamic Lorentz force law

What are the fundamental limitations for finite-time engines that extract work from active nonequilibrium systems, and what are the optimal protocols that approach them? We show that the finite-time work extraction for nonconservative overdamped Langevin systems may be rewritten as a Lorentz force Lagrangian action, with the kinetic term corresponding to a thermodynamic metric term that is an $L_2$-optimal transport cost for the time-dependent probability density, and the magnetic field coupling term corresponding to an effective quasistatic work extraction, proving that optimal protocols counterdiabatically steer the thermodynamic state trajectory to satisfy a Lorentz force law defined on thermodynamic state space. We utilize and reinterpret classic concepts from electromagnetism in the setting of cyclical nonequilibrium processes. We show that the housekeeping heat can be controlled to be arbitrarily close to zero by minimizing nonequilibrium fluctuations. It immediately follows from our results that the constant-velocity angle clamp protocol applied to the $F_1$ molecular motor in a recent experiment [Mishima et at, 2025] is in fact the globally optimal protocol: it produces zero housekeeping heat while simultaneously minimizing dissipation and maximizing work transduction.

cond-mat.stat-mech↗

arXiv2026

Higher-order response theory in optimal stochastic thermodynamics

Linear response theory has found many applications in statistical physics. One of these is to compute minimal-work protocols that drive nonequilibrium systems between different thermodynamic states, which are useful for designing engineered nanoscale systems and understanding biomolecular machines. We compare and explore the relationships between linear-response-based approximations used to study optimal protocols in different driving regimes by showing that they arise as controlled truncations of a general causal response (Volterra) expansion. We then construct higher-order response terms and discuss the drawbacks and utility of their inclusion. We illustrate our results for an overdamped particle in a harmonic trap, ultimately showing that the inclusion of higher-order response in calculating optimal protocols provides marginal improvement in effectiveness despite incurring a significant computational expense, while introducing the possibility of predicting arbitrarily low and unphysical negative excess work.

cond-mat.stat-mech↗

arXiv2025

Transporting Baguettes With Minimal Action: The Geometry of Optimal Nonequilibrium Processes in Stochastic Thermodynamics

What are the fundamental limitations placed by the laws of thermodynamics on the energy expenditure needed to carry out a given task in a nonequilibrium environment in finite time? In this thesis, we investigate "optimal nonequilibrium processes": how nonequilibrium state changes in a thermodynamic system may be performed most efficiently, in the sense of requiring the least amount of thermodynamic work. Surprisingly, there is a hidden, fundamental geometric structure in this optimization problem that is related to the mathematics of optimal transport theory: how to optimally send, e.g., baguettes from bakeries to cafés, given supply and demand constraints, that requires the least amount of total distance traveled by the baguettes. After giving a brief overview on the mathematical framework of stochastic thermodynamics for the overdamped Langevin equation, we present a trio of works: (1) applying optimal control theory to the Fokker-Planck equation to calculate exact optimal protocols for low-dimensional systems, which reproduces the intriguing previously-discovered discontinuities in globally optimal protocols and reveals new non-monotonic optimal protocols for a certain system; (2) exploiting the importance sampling of Langevin trajectories under different protocols, to adaptively optimize protocols by controlling the thermodynamic state trajectory, which is useful for efficiently calculating free energy differences between different Hamiltonians; and finally, (3) deriving an exact geometric description of optimal nonequilibrium processes and a geodesic-counterdiabatic decomposition for the optimal protocols that enact them, which satisfyingly explains the highly non-intuitive properties of discontinuities and possible non-monotonicity in globally optimal protocols.

cond-mat.stat-mech↗

arXiv2024

Limitations from charge quantization on the parallel temperature diagnostic of nonneutral plasmas

We develop a new algorithm to estimate the temperature of a nonneutral plasma in a Penning-Malmberg trap. The algorithm analyzes data obtained by slowly lowering a voltage that confines one end of the plasma and collecting escaping charges, and is a maximum likelihood estimator based on a physically-motivated model of the escape protocol presented in Beck [1990]. Significantly, our algorithm may be used on single-count data, allowing for improved fits with low numbers of escaping electrons. This is important for low-temperature plasmas such as those used in antihydrogen trapping. We perform a Monte Carlo simulation of our algorithm, and assess its robustness to intrinsic shot noise and external noise. Approximately 100 particle counts are needed for an accuracy of +/-10% -- this provides a lower bound for measurable plasma temperatures of approximately 3 K for plasmas of length 1 cm.

physics.plasm-ph↗

arXiv2024

Beyond Linear Response: Equivalence between Thermodynamic Geometry and Optimal Transport

A fundamental result of thermodynamic geometry is that the optimal, minimal-work protocol that drives a nonequilibrium system between two thermodynamic states in the slow-driving limit is given by a geodesic of the friction tensor, a Riemannian metric defined on control space. For overdamped dynamics in arbitrary dimensions, we demonstrate that thermodynamic geometry is equivalent to $L^2$ optimal transport geometry defined on the space of equilibrium distributions corresponding to the control parameters. We show that obtaining optimal protocols past the slow-driving or linear response regime is computationally tractable as the sum of a friction tensor geodesic and a counterdiabatic term related to the Fisher information metric. These geodesic-counterdiabatic optimal protocols are exact for parameteric harmonic potentials, reproduce the surprising non-monotonic behavior recently discovered in linearly-biased double well optimal protocols, and explain the ubiquitous discontinuous jumps observed at the beginning and end times.

cond-mat.stat-mech↗

arXiv2023

Time-Asymmetric Fluctuation Theorem and Efficient Free Energy Estimation

The free-energy difference $ΔF$ between two high-dimensional systems is notoriously difficult to compute, but very important for many applications, such as drug discovery. We demonstrate that an unconventional definition of work introduced by Vaikuntanathan and Jarzynski (2008) satisfies a microscopic fluctuation theorem that relates path ensembles that are driven by protocols unequal under time-reversal. It has been shown before that counterdiabatic protocols -- those having additional forcing that enforces the system to remain in instantaneous equilibrium, also known as escorted dynamics or engineered swift equilibration -- yield zero-variance work measurements for this definition. We show that this time-asymmetric microscopic fluctuation theorem can be exploited for efficient free energy estimation by developing a simple (i.e., neural-network free) and efficient adaptive time-asymmetric protocol optimization algorithm that yields $ΔF$ estimates that are orders of magnitude lower in mean squared error than the generic linear interpolation protocol with which it is initialized.

cond-mat.soft↗

arXiv2022

Limited-control optimal protocols arbitrarily far from equilibrium

Recent studies have explored finite-time dissipation-minimizing protocols for stochastic thermodynamic systems driven arbitrarily far from equilibrium, when granted full external control to drive the system. However, in both simulation and experimental contexts, systems often may only be controlled with a limited set of degrees of freedom. Here, going beyond slow- and fast-driving approximations employed in previous studies, we obtain exact finite-time optimal protocols for this unexplored limited-control setting. By working with deterministic Fokker-Planck probability density time evolution, we can frame the work-minimizing protocol problem in the standard form of an optimal control theory problem. We demonstrate that finding the exact optimal protocol is equivalent to solving a system of Hamiltonian partial differential equations, which in many cases admit efficiently calculatable numerical solutions. Within this framework, we reproduce analytical results for the optimal control of harmonic potentials, and numerically devise novel optimal protocols for two anharmonic examples: varying the stiffness of a quartic potential, and linearly biasing a double-well potential. We confirm that these optimal protocols outperform other protocols produced through previous methods, in some cases by a substantial amount. We find that for the linearly biased double-well problem, the mean position under the optimal protocol travels at a near-constant velocity. Surprisingly, for a certain timescale and barrier height regime, the optimal protocol is also non-monotonic in time.

cond-mat.stat-mech↗

arXiv2022

Engineered swift equilibration for arbitrary geometries

Engineered swift equilibration (ESE) is a class of driving protocols that enforce an equilibrium distribution with respect to external control parameters at the beginning and end of rapid state transformations of open, classical non-equilibrium systems. ESE protocols have previously been derived and experimentally realized for Brownian particles in simple, one-dimensional, time-varying trapping potentials; one recent study considered ESE in two-dimensional Euclidean configuration space. Here we extend the ESE framework to generic, overdamped Brownian systems in arbitrary curved configuration space and illustrate our results with specific examples not amenable to previous techniques. Our approach may be used to impose the necessary dynamics to control the full temporal configurational distribution in a wide variety of experimentally realizable settings.

cond-mat.stat-mech↗