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 sub-space. 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 sub-space, 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.
Highlights
Biological systems in general operate out of equilibrium [1]
Particles diffusing in a solution that can be connected to different baths follow a FokkerPlanck equation [8,9,10], while the switching between baths is controlled by a different process
We show that in cases analogous to (i) the single index approximation (SIA) leads to a well-known formula reported in the literature [5,20], whereas in cases belonging to the classes (ii) and (iii) additional terms arise due to the interplay between nonequilibrium stationarity and the time scale of the fastest process
Summary
Biological systems in general operate out of equilibrium [1]. These can be described in terms of different states (both discrete and continuous), which are connected to each other through a set of transitions with given rates. Without loss of generality, we will consider the dynamics in the ν space to be faster than the one in the i space, unless otherwise stated Since these models allow for a complete description of systems out of equilibrium, the main focus of this work is to study the net production of entropy in the surroundings, which is one of the fingerprints of a nonequilibrium condition [17,23,24,25]. The most general approach is to evaluate the entropy production by considering all processes acting on similar time scales [42,43,44,45,46,47,48] In this case, the result is devoid of approximations. Well-known formulas presented in literature as general results emerge from our framework only under some limiting conditions
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