Non-equilibrium Markov state modeling of periodically driven biomolecules

Oscillating states of driven Langevin systems under large viscous drives

We provide a perturbative scheme that is suitable to study oscillating states in driven Langevin systems in the large viscous regime. We explicitly determine the oscillating state distribution of an underdamped Brownian particle driven by a time-dependent periodic potential. Apart from the harmonic and anharmonic parameters of the potential, the noise strength and the viscous parameter (or equivalently their ratio referred to as the thermal parameter), which appear in the dynamics of the Brownian particle, are also driven periodically. We specify various nonequilibrium observables, relevant to characterize the oscillating states, and evaluate them to linear order in anharmonic perturbation. We find that the effect of viscous drives on oscillating states is measurable even at leading order and show that the thermodynamic properties of the system in these states are significantly distinct from those in equilibrium or even from those exhibited by oscillating states of overdamped driven systems.

Modeling of biomolecular machines in non-equilibrium steady states

Numerical computations have become a pillar of all modern quantitative sciences. Any computation involves modeling-even if often this step is not made explicit-and any model has to neglect details while still being physically accurate. Equilibrium statistical mechanics guides both the development of models and numerical methods for dynamics obeying detailed balance. For systems driven away from thermal equilibrium, such a universal theoretical framework is missing. For a restricted class of driven systems governed by Markov dynamics and local detailed balance, stochastic thermodynamics has evolved to fill this gap and to provide fundamental constraints and guiding principles. The next step is to advance stochastic thermodynamics from simple model systems to complex systems with tens of thousands or even millions of degrees of freedom. Biomolecules operating in the presence of chemical gradients and mechanical forces are a prime example for this challenge. In this Perspective, we give an introduction to isothermal stochastic thermodynamics geared toward the systematic multiscale modeling of the conformational dynamics of biomolecular and synthetic machines, and we outline some of the open challenges.

Excess and loss of entropy production for different levels of coarse graining

We investigate the effect of coarse graining on the thermodynamic properties of a system, focusing on entropy production. As a case of study, we consider a one-dimensional colloidal particle in contact with a thermal bath, moving in a sinusoidal potential and driven out of equilibrium by a small constant force. Different levels of coarse graining are evaluated: At first, we compare the results in the underdamped dynamics with those in the overdamped one (first coarse graining). For large values of the friction coefficient, the two dynamics have the same thermodynamics properties, while, for smaller friction values, the overdamped approximation produces an excess of entropy production with respect to that of the underdamped dynamics. Moreover, for further smaller values of the drag coefficient, the excess of entropy production turns into a loss. These regimes are explained by evaluating the jump statistics, observing that the inertia is able to induce multiple jumps and affect the average jump rate. The periodic shape of the potential allows us to approximate the continuous dynamics via a Markov chain after the introduction of a suitable time and space discretization (second level of coarse graining). This discretization procedure is implemented starting both from the underdamped and the overdamped evolution and is analyzed for different values of the friction coefficient.

Oscillating states of periodically driven anharmonic Langevin systems

We investigate the asymptotic distributions of periodically driven anharmonic Langevin systems. Utilizing the underlying SL_{2} symmetry of the Langevin dynamics, we develop a perturbative scheme in which the effect of periodic driving can be treated nonperturbatively to any order of perturbation in anharmonicity. We spell out the conditions under which the asymptotic distributions exist and are periodic and show that the distributions can be determined exactly in terms of the solutions of the associated Hill equations. We further find that the oscillating states of these driven systems are stable against anharmonic perturbations.

Periodically driven harmonic Langevin systems

Motivated to understand the asymptotic behavior of periodically driven thermodynamic systems, we study the prototypical example of Brownian particle, overdamped and underdamped, in harmonic potentials subjected to periodic driving. The harmonic strength and the coefficients of drift and diffusion are all taken to be T-periodic. We obtain the asymptotic distributions almost exactly treating driving nonperturbatively. In the underdamped case, we exploit the underlying SL_{2} symmetry to obtain the asymptotic state, and to study the dynamics and fluctuations of energies and entropy. We further obtain the two-time correlation functions and investigate the responses to drift and diffusion perturbations in the presence of driving.

Imitating nonequilibrium steady states using time-varying equilibrium force in many-body diffusive systems

An equivalence between nonequilibrium steady states (NESS) driven by a time-independent force and stochastic pumps (SP) stirred by a time-varying conservative force is studied for general many-body diffusive systems. When the particle density and current of NESS are imitated by SP time-averaged counterparts, we prove that the entropy production rate in the SP is always greater than that of the NESS, provided that the conductivity of the particle current is concave as a function of the particle density. Searching for a SP protocol that saturates the entropy production bound reveals an unexpected connection with traffic waves, where a high density region propagates against the direction of the particle current.