2004/05/31 by F. Ritort, Félix Ritort · 2 citations
Chemistry · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #cond-mat.mtrl-sci #cond-mat.stat-mech #stochastic dynamics and bifurcation #thermodynamics and calorimetric analyses
paper · pdf · doi:10.1088/1742-5468/2004/10/p10016
28 pages, 14 figures (Latex)
arxiv created 2004/05/31 · openalex publication_date 2004/10/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Two-state models provide phenomenological descriptions of many different systems, ranging from physics to chemistry and biology. We investigate work fluctuations in an ensemble of two-state systems driven out of equilibrium under the action of an external perturbation. We calculate the probability density P N ( W ) that work equal to W is exerted upon the system (of size N ) along a given non-equilibrium trajectory and introduce a trajectory thermodynamics formalism to quantify work fluctuations in the large- N limit. We then define a trajectory entropy S N ( W ) that counts the number of non-equilibrium trajectories P N ( W ) = exp( S N ( W )/ k B T ) with work equal to W and characterizes fluctuations of work trajectories around the most probable value W mp . A trajectory free energy can also be defined, which has a minimum at W = W † , this being the value of the work that has to be efficiently sampled to quantitatively test the Jarzynski equality. Within this formalism a Lagrange multiplier is also introduced, the inverse of which plays the role of a trajectory temperature . Our general solution for P N ( W ) exactly satisfies the fluctuation theorem by Crooks and allows us to investigate heat fluctuations for a protocol that is invariant under time reversal. The heat distribution is then characterized by a Gaussian component (describing small and frequent heat exchange events) and exponential tails (describing the statistics of large deviations and rare events). For the latter, the width of the exponential tails is related to the aforementioned trajectory temperature . Finite-size effects to the large- N theory and the recovery of work distributions for finite N are also discussed. Finally, we pay particular attention to the case of magnetic nanoparticle systems under the action of a magnetic field H where work and heat fluctuations are predicted to be observable in ramping experiments in micro-SQUIDs.