Monotonicity of the dynamical activity

Abstract

The Donsker-Varadhan rate function for occupation-time fluctuations has been seen numerically to exhibit monotone return to stationary nonequilibrium [Phys. Rev. Lett. 107, 010601 (2011)]. That rate function is related to dynamical activity and, except under detailed balance, it does not derive from the relative entropy for which the monotonicity in time is well understood. We give a rigorous argument that the Donsker-Varadhan function is indeed monotone under the Markov evolution at large enough times with respect to the relaxation time, provided that a "normal linear-response" condition is satisfied.

19 pages, 1 figure; v3: Section I extended, 3 references added

References in corpus (7)

• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Space-time thermodynamics and subsystem observables in a kinetically constrained model of glassy systems
• Thermodynamic formula for the cumulant generating function of time-averaged current
• Minimum entropy production principle from a dynamical fluctuation law
• Monotone return to steady nonequilibrium
• Infinite family of second-law-like inequalities
• Static and dynamical nonequilibrium fluctuations

Cited by in corpus (6)

• Frenesy: time-symmetric dynamical activity in nonequilibria
• Improving the convergence of reversible samplers
• Canonical structure and orthogonality of forces and currents in irreversible Markov chains
• Nonconvexity of the relative entropy for Markov dynamics: A Fisher information approach
• Revisiting the Glansdorff-Prigogine criterion for stability within irreversible thermodynamics
• Fisher information of Markovian decay modes - Nonequilibrium equivalence principle, dynamical phase transitions and coarse graining