Abstract
ABSTRACT The second law of thermodynamics imposes an increase of macroscopic entropy with time in an isolated system. Microscopically, however, the entropy production can be negative for a single, microscopic realization of a thermodynamic process. The so-called fluctuation theorems provide exact relations between the stochastic entropy consumption and generation. Here, we analyse pixel-to-pixel fluctuations in time of small-scale magnetic fields (SSMF) in the quiet Sun observed with the SDO/HMI instrument. We demonstrate that entropy generated by SSMF obeys the fluctuation theorems. In particular, the SSMF entropy consumption probability is exactly exponentially smaller than the SSMF entropy generation probability. This may have fundamental implications for the magnetic energy budget of the Sun.
Highlights
Studying spatial and temporal dynamics of small-scale magnetic fields (SSMF) on the solar surface is important for system-wide understanding of the solar magnetism and its role in heating the solar outer atmosphere
This iteration is repeated after shifting the two-image-stencil to the position in time by the ∆t-step, so that the pair of images is at times t + ∆t and t + 2∆t
We have shown that the fundamental fluctuation theorems (FTs) discovered both theoretically and experimentally in the framework of stochastic thermodynamics are valid for evolution of solar SSMF
Summary
Studying spatial and temporal dynamics of small-scale magnetic fields (SSMF) on the solar surface is important for system-wide understanding of the solar magnetism and its role in heating the solar outer atmosphere. In this Letter, we employ a novel formalism which abandons the idea of ’magnetic features’ and treats pixel-wise the photospheric magnetic flux density concentrations as homogeneous patches of a flowing substance (field). This approach was recently developed by Gorobets et al (2016) and Gorobets et al (2017) (hereafter Paper I and Paper II), who established that (1) line-of-site (BLOS ) and longitudinal components of SSMF density evolve as Markov chains (Paper I), (2) SSMF is a phenomenological thermodynamic system in a non-equilibrium state (NS, Paper II), and (3) the observed NS thermalizes into a state with a maximum of the informationtheoretic entropy (Paper II). We develop further this thermodynamic approach to study dynamics of SSMF
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