We slightly extend the fluctuation theorem obtained in (Lebowitz and Spohn in J. Stat. Phys. 95:333-365, 1999) for sums of generators, considering continuous-time Markov chains on a finite state space whose underlying graph has multiple edges and no loop. This extended frame is suited when analyzing chemical systems. As simple corollary we derive by a different method the fluctuation theorem of D. Andrieux and P. Gaspard for the fluxes along the chords associated to a fundamental set of oriented cycles (Andrieux and Gaspard in J. Stat. Phys. 127:107-131, 2007). We associate to each random trajectory an oriented cycle on the graph and we decompose it in terms of a basis of oriented cycles. We prove a fluctuation theorem for the coefficients in this decomposition. The resulting fluctuation theorem involves the cycle affinities, which in many real systems correspond to the macroscopic forces. In addition, the above decomposition is useful when analyzing the large deviations of additive functionals of the Markov chain. As example of application, in a very general context we derive a fluctuation relation for the mechanical and chemical currents of a molecular motor moving along a periodic filament.

Gallavotti-Cohen-Type Symmetry Related to Cycle Decompositions for Markov Chains and Biochemical Applications / Faggionato, Alessandra; D., Di Pietro. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 143:1(2011), pp. 11-32. [10.1007/s10955-011-0161-7]

Gallavotti-Cohen-Type Symmetry Related to Cycle Decompositions for Markov Chains and Biochemical Applications

FAGGIONATO, ALESSANDRA;
2011

Abstract

We slightly extend the fluctuation theorem obtained in (Lebowitz and Spohn in J. Stat. Phys. 95:333-365, 1999) for sums of generators, considering continuous-time Markov chains on a finite state space whose underlying graph has multiple edges and no loop. This extended frame is suited when analyzing chemical systems. As simple corollary we derive by a different method the fluctuation theorem of D. Andrieux and P. Gaspard for the fluxes along the chords associated to a fundamental set of oriented cycles (Andrieux and Gaspard in J. Stat. Phys. 127:107-131, 2007). We associate to each random trajectory an oriented cycle on the graph and we decompose it in terms of a basis of oriented cycles. We prove a fluctuation theorem for the coefficients in this decomposition. The resulting fluctuation theorem involves the cycle affinities, which in many real systems correspond to the macroscopic forces. In addition, the above decomposition is useful when analyzing the large deviations of additive functionals of the Markov chain. As example of application, in a very general context we derive a fluctuation relation for the mechanical and chemical currents of a molecular motor moving along a periodic filament.
2011
oriented cycle; generating function; thermodynamic force; spanning tree; nonequilibrium steady state; large deviation; molecular motor; affinity; fluctuation theorem
01 Pubblicazione su rivista::01a Articolo in rivista
Gallavotti-Cohen-Type Symmetry Related to Cycle Decompositions for Markov Chains and Biochemical Applications / Faggionato, Alessandra; D., Di Pietro. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 143:1(2011), pp. 11-32. [10.1007/s10955-011-0161-7]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/379608
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