arXiv subjects

David A Sivak

Publications and source records attributed to David A Sivak.

8 recordsLinked to original sources

arXiv2026

Thermodynamic geometry of friction on graphs: Resistance, commute times, and optimal transport

We demonstrate that the thermodynamic friction metric governing dissipation in slowly driven continuous-time Markov chains is equivalent to the commute-time embedding and the resistance distance. This equivalence yields complementary insights: The commute-time embedding demonstrates the intrinsic cost of transporting probability across dynamical bottlenecks, while the resistance distance maps thermodynamic dissipation to Joule heating in an electrical network. We further demonstrate that the linear-response thermodynamic distance is a discrete $L^2$-Wasserstein optimal transport cost evaluated along paths of equilibrium distributions, extending a continuous-state correspondence to discrete networks. This conceptual synthesis of linear-response thermodynamics, random walks on graphs, electrical circuits, and optimal-transport theory connects independently developed geometric frameworks, reduces complex metric calculations to simple circuit algebra, and provides a clear physical picture of dissipation as the energetic cost of routing probability through the state space network.

cond-mat.stat-mech↗

arXiv2021

Free-energy transduction within autonomous systems

The excess work required to drive a stochastic system out of thermodynamic equilibrium through a time-dependent external perturbation is directly related to the amount of entropy produced during the driving process, allowing excess work and entropy production to be used interchangeably to quantify dissipation. Given the common intuition of biological molecular machines as internally communicating work between components, it is tempting to extend this correspondence to the driving of one component of an autonomous system by another; however, no such relation between the internal excess work and entropy production exists. Here we introduce the `transduced additional free energy rate' between strongly coupled subsystems of an autonomous system, that is analogous to the excess power in systems driven by an external control parameter that receives no feedback from the system. We prove that this is a relevant measure of dissipation -- in that it equals the steady-state entropy production rate due to the downstream subsystem -- and demonstrate its advantages with a simple model system.

cond-mat.stat-mech↗

arXiv2021

Hidden energy flows in strongly coupled nonequilibrium systems

Quantifying the flow of energy within and through fluctuating nanoscale systems poses a significant challenge to understanding microscopic biological machines. A common approach involves coarse-graining, which allows a simplified description of such systems. This has the side effect of inducing so-called hidden contributions (due to sub-resolution dynamics) that complicate the resulting thermodynamics. Here we develop a thermodynamically consistent theory describing the nonequilibrium excess power internal to autonomous systems, and introduce a phenomenological framework to quantify the hidden excess power associated with their operation. We confirm our theoretical predictions in numerical simulations of a minimal model for both a molecular transport motor and a rotary motor.

cond-mat.stat-mech↗

arXiv2019

Theory of nonequilibrium free energy transduction by molecular machines

Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared to more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.

cond-mat.stat-mech↗

arXiv2019

Pulling cargo increases the precision of molecular motor progress

Biomolecular motors use free energy to drive a variety of cellular tasks, including the transport of cargo, such as vesicles and organelles. We find that the widely-used `constant-force' approximation for the effect of cargo on motor dynamics leads to a much larger variance of motor step number compared to explicitly modeling diffusive cargo, suggesting the constant-force approximation may be misapplied in some cases. We also find that, with cargo, motor progress is significantly more precise than suggested by a recent result. For cargo with a low relative diffusivity, the dynamics of continuous cargo motion---rather than discrete motor steps---dominate, leading to a new, more permissive bound on the precision of motor progress which is independent of the number of stages per motor cycle.

cond-mat.stat-mech↗

arXiv2017

Allocating and splitting free energy to maximize molecular machine flux

Biomolecular machines transduce between different forms of energy. These machines make directed progress and increase their speed by consuming free energy, typically in the form of nonequilibrium chemical concentrations. Machine dynamics are often modeled by transitions between a set of discrete metastable conformational states. In general, the free energy change associated with each transition can increase the forward rate constant, decrease the reverse rate constant, or both. In contrast to previous optimizations, we find that in general flux is neither maximized by devoting all free energy changes to increasing forward rate constants nor by solely decreasing reverse rate constants. Instead the optimal free energy splitting depends on the detailed dynamics. Extending our analysis to machines with vulnerable states (from which they can break down), in the strong driving corresponding to in vivo cellular conditions, processivity is maximized by reducing the occupation of the vulnerable state.

cond-mat.stat-mech↗

arXiv2017

Allocating dissipation across a molecular machine cycle to maximize flux

Biomolecular machines consume free energy to break symmetry and make directed progress. Nonequilibrium ATP concentrations are the typical free energy source, with one cycle of a molecular machine consuming a certain number of ATP, providing a fixed free energy budget. Since evolution is expected to favor rapid-turnover machines that operate efficiently, we investigate how this free energy budget can be allocated to maximize flux. Unconstrained optimization eliminates intermediate metastable states, indicating that flux is enhanced in molecular machines with fewer states. When maintaining a set number of states, we show that---in contrast to previous findings---the flux-maximizing allocation of dissipation is not even. This result is consistent with the coexistence of both `irreversible' and reversible transitions in molecular machine models that successfully describe experimental data, which suggests that in evolved machines different transitions differ significantly in their dissipation.

cond-mat.stat-mech↗

arXiv2017

Toward the design principles of molecular machines

Living things avoid equilibrium using molecular machines. Such microscopic soft-matter objects encounter relatively large friction and fluctuations. We discuss design principles for effective molecular machine operation in this unfamiliar context.

cond-mat.stat-mech↗