Local discretization method for overdamped Brownian motion on a potential with multiple deep wells

Virial-like thermodynamic uncertainty relation in the tight-binding regime

We presented a methodology to approximate the entropy production for Brownian motion in a tilted periodic potential. The approximation stems from the well known thermodynamic uncertainty relation. By applying a virial-like expansion, we provided a tighter lower limit solely in terms of the drift velocity and diffusion. The approach presented is systematically analyzed in the tight-binding regime. We also provide a relative simple rule to validate using the tight-binding approach based on drift and diffusion relations rather than energy barriers and forces. We also discuss the implications of our results outside the tight-binding regime.

A model of minimal entropy generation for cytoskeletal transport systems with multiple interacting motors

We study the steady-state rate of entropy generation for multiple interacting particles. The description used is based on the partially asymmetric exclusion process in a lattice with periodic boundary conditions. Our methodology shows that in the steady-state, the rate of entropy generation is directly proportional to the bulk drift and the applied driving force. Since in many cases the driving force is unknown or hard to determine. We circumvent this by deriving a lower bound for the entropy, resulting in an extended thermodynamic uncertainty relation for the asymmetric simple exclusion process. We systematically compared this bound with the actual entropy generation. Thus, we identify the force regimes, and particles' density conditions where the entropy bound derived from this extended thermodynamic uncertainty relation is meaningful.

Nonequilibrium master equation for interacting Brownian particles in a deep-well periodic potential

Employing a creation and annihilation operator formulation, we derive an approximate many-body master equation describing discrete hopping from the more general continuous description of Brownian motion on a deep-well nonequilibrium periodic potential. The many-body master equation describes interactions of arbitrary strength and range arising from a "top-hat" two-body interaction potential. We show that this master equation reduces to the well-known asymmetric simple exclusion process and the zero range process in certain regimes. We also use the creation and annihilation operator formalism to derive results for the steady-state drift and the number fluctuations in special cases, including the unexplored limit of weak interparticle interactions.

Tight-binding derivation of a discrete-continuous description of mechanochemical coupling in a molecular motor

We present a tight-binding derivation of a discrete-continuous description of mechanochemical coupling in a molecular motor. Our derivation is based on the continuous diffusion equation for overdamped Brownian motion on a time-independent tilted periodic potential in two dimensions. The free-energy potential is nonseparable to allow coupling between the chemical and mechanical degrees of freedom. We formally discretize the chemical coordinate by expanding in Wannier states that are localized along the chemical coordinate and parametrized along the mechanical coordinate. A discrete-continuous equation is derived that is valid for anisotropic systems with weak mechanochemical coupling and deep potential wells along the chemical coordinate. The discrete-continuous description is consistent with established theoretical models of molecular motors with discrete chemical states but is constrained by the underlying continuous two-dimensional potential. In particular, we derive analytic expressions for the effective potential along the mechanical coordinate and for the rate of thermal hopping between chemical states. We determine the thermodynamic efficiency of energy conversion and find that, for a molecular motor with one chemical state per cycle, the derived discrete-continuous equation can accurately describe mechanochemical coupling but cannot describe energy conversion.