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Entropy Production by Logarithmic Decomposition

In statistical physics, entropy is generally logarithm of probability. Therefore, if dynamics is decomposed by log, entropy production should be decomposed properly. In the present work, log-decomposition of dynamics is introduced. By which time evolution operator is logarithmically decomposed into a symmetric operator and an asymmetric factor. Path probability and path entropy production are also systematically and intuitively decomposed into symmetric and asymmetric parts. From symmetric operator, non-adiabatic entropy production is derived, whereas adiabatic entropy production is from asymmetric factor.