{'fraction_non_alphanumeric': 0.020348837209302327, 'fraction_numerical': 0.0, 'mean_word_length': 5.689320388349515, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Einstein’s fluctuation relation and Gibbs states far from equilibrium

We examine a class of one-dimensional lattice-gases characterised by a gradient condition which is a necessary and sufficient condition for the existence of Gibbs-type homogeneous stationary states. We show how, defining appropriate boundary conditions, this condition leads to a novel fluctuation relation under reservoir exchange, unrelated to the Gallavotti–Cohen symmetry. We show that it can be interpreted as a nonequilibrium and nonlinear generalisation of Einstein’s relation, leading to Onsager reciprocity relations in the limit of a small reservoir imbalance. We illustrate these results with two examples.