**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Publication# Coarse-grained entropy production with multiple reservoirs: Unraveling the role of time scales and detailed balance in biology-inspired systems

Abstract

A general framework to describe a vast majority of biology-inspired systems is to model them as stochastic processes in which multiple couplings are in play at the same time. Molecular motors, chemical reaction networks, catalytic enzymes, and particles exchanging heat with different baths, constitute some interesting examples of such a modelization. Moreover, they usually operate out of equilibrium, being characterized by a net production of entropy, which entails a constrained efficiency. Hitherto, in order to investigate multiple processes simultaneously driving a system, all theoretical approaches deal with them independently, at a coarse-grained level, or employing a separation of time scales. Here, we explicitly take in consideration the interplay among time scales of different processes and whether or not their own evolution eventually relaxes toward an equilibrium state in a given subspace. We propose a general framework for multiple coupling, from which the well-known formulas for the entropy production can be derived, depending on the available information about each single process. Furthermore, when one of the processes does not equilibrate in its subspace, even if much faster than all the others, it introduces a finite correction to the entropy production. We employ our framework in various simple and pedagogical examples, for which such a corrective term can be related to a typical scaling of physical quantities in play.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts

Loading

Related publications

Loading

Related concepts (19)

Entropy production

Entropy production (or generation) is the amount of entropy which is produced during heat process to evaluate the efficiency of the process.
Short history
Entropy is produced in irrevers

Entropy

Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in

Time

Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component

Related publications (7)

Loading

Loading

Loading

Daniel Maria Busiello, Amos Maritan

Systems out of equilibrium exhibit a net production of entropy. We study the dynamics of a stochastic system represented by a Master equation (ME) that can be modeled by a Fokker-Planck equation in a coarse-grained, mesoscopic description. We show that the corresponding coarse-grained entropy production contains information on microscopic currents that are not captured by the Fokker-Planck equation and thus cannot be deduced from it. We study a discrete-state and a continuous-state system, deriving in both the cases an analytical expression for the coarse-graining corrections to the entropy production. This result elucidates the limits in which there is no loss of information in passing from a ME to a Fokker-Planck equation describing the same system. Our results are amenable of experimental verification, which could help to infer some information about the underlying microscopic processes.

2019Daniel Maria Busiello, Amos Maritan

The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenberg's work and hitherto can be carried out when for each transition between two states also the reverse one is allowed. Nevertheless, several physical systems may exhibit a mixture of both unidirectional and bidirectional transitions, and how to properly define the entropy production, in this case, is still an open question. Here, we present a solution to such a challenging problem. The average entropy production can be consistently defined, employing a mapping that preserves the average fluxes, and its physical interpretation is provided. We describe a class of stochastic systems composed of unidirectional links forming cycles and detailed-balanced bidirectional links, showing that they behave in a pseudo-deterministic fashion. This approach is applied to a system with time-dependent stochastic resetting. Our framework is consistent with thermodynamics and leads to some intriguing observations on the relation between the arrow of time and the average entropy production for resetting events.

2020Sara Dal Cengio, Ignacio Pagonabarraga Mora

We present a comprehensive study about the relationship between the way detailed balance is broken in non-equilibrium systems and the resulting violations of the fluctuation-dissipation theorem. Starting from stochastic dynamics with both odd and even variables under time-reversal, we derive an explicit expression for the time-reversal operator, i.e. the Markovian operator which generates the time-reversed trajectories. We then exploit the relation between entropy production and the breakdown of detailed balance to establish general constraints on the non-equilibrium steady-states (NESS), which relate the non-equilibrium character of the dynamics with symmetry properties of the NESS distribution. This provides a direct route to derive extended fluctuation-dissipation relations, expressing the linear response function in terms of NESS correlations. Such framework provides a unified way to understand the departure from equilibrium of active systems and its linear response. We then consider two paradigmatic models of interacting self-propelled particles, namely active Brownian particles and active Ornstein-Uhlenbeck particles. We analyze the non-equilibrium character of these systems (also within a Markov and a Chapman-Enskog approximation) and derive extended fluctuation-dissipation relations for them, clarifying which features of these active model systems are genuinely non-equilibrium.