2015/02/01 by Peter Burgholzer, Burgholzer, Peter · 1 citation
Environmental Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Ecosystem dynamics and resilience #FOS: Physical sciences #Quantum Mechanics and Applications #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1502.00214
openalex publication_date 2015/02/01 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28
In macroscopic systems behavior is usually reproducible and fluctuations,\nwhich are deviations from the typically observed mean values, are small. But\nalmost all inverse problems in the physical and biological sciences are\nill-posed and these fluctuations are highly 'amplified'. Using stochastic\nthermodynamics we describe a system in equilibrium kicked to a state far from\nequilibrium and the following dissipative process back to equilibrium. From the\nobserved value at a certain time after the kick the magnitude of the kick\nshould be estimated, which is such an ill-posed inverse problem and\nfluctuations get relevant. For the model system of a kicked Brownian particle\nthe time-dependent probability distribution, the information loss about the\nmagnitude of the kick described by the Kullback-Leibler divergence, and the\nentropy production derived from the observed mean values are given. The\nequality of information loss caused by fluctuations and mean entropy production\nis shown for general kicked dissipative processes from stochastic\nthermodynamics following the derivation of the Jarzynski and Crooks equalities.\nThe information-theoretical interpretation of the Kullback-Leibler divergence\n(Chernoff-Stein Lemma) allows us to describe the influence of the fluctuations\nwithout knowing their distributions just from the mean value equations and thus\nto derive very applicable results, e.g., by giving thermodynamic limits of\nspatial resolution for imaging.\n