General no-go condition for stochastic pumping

Abstract

The control of chemical dynamics requires understanding the effect of time-dependent transition rates between states of chemo-mechanical molecular configurations. Pumping refers to generating a net current, e.g. per period in the time-dependence, through a cycle of consecutive states. The working of artificial machines or synthesized molecular motors depends on it. In this paper we give short and simple proofs of no-go theorems, some of which appeared before but here with essential extensions to non-Markovian dynamics, including the study of the diffusion limit. It allows to exclude certain protocols in the working of chemical motors where only the depth of the energy well is changed in time and not the barrier height between pairs of states. We also show how pre-existing steady state currents are in general modified with a multiplicative factor when this time-dependence is turned on.

8 pages; v2: minor changes, 1 reference added

References in corpus (5)

• Directed flow in non-adiabatic stochastic pumps
• The unified geometric theory of mesoscopic stochastic pumps and reversible ratchets
• Pumping-Restriction Theorem for Stochastic Networks
• Exact formula for currents in strongly pumped diffusive systems
• Robust quantization of a molecular motor motion in a stochastic environment

Cited by in corpus (19)

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• Level 2.5 large deviations for continuous time Markov chains with time periodic rates
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• Stochastic thermodynamics of periodically driven systems: Fluctuation theorem for currents and unification of two classes
• Similarities and Differences Between Nonequilibrium Steady States and Time-Periodic Driving in Diffusive Systems
• Fluctuation Relations for Current Components in Mesoscopic Electric Circuits
• Duality and fluctuation relations for statistics of currents on cyclic graphs
• Linear Stochastic Thermodynamics
• Unification and new extensions of the no-pumping theorems of stochastic pumps
• Geometric Universality of Currents
• Hybrid models of molecular machines and the no-pumping theorem
• Imitating non-equilibrium steady states using time-varying equilibrium force in many-body diffusive systems
• No-pumping theorem for non-Arrhenius rates
• The validity of the no-pumping theorem in systems with finite-range interactions between particles