Stochastic thermodynamics assigns work, heat, and entropy production to individual fluctuating trajectories while recovering ordinary thermodynamics after ensemble averaging.
Local detailed balance states that the logarithm of the probability ratio between a trajectory and its time reverse equals the entropy delivered to the environment in units of . For one heat bath, when positive flows into the bath.
Entropy production is the sum of the entropy changes of a system and its environment. Under local detailed balance it is represented by a forward-to-reversed path-probability logarithm and has nonnegative expectation.
For a Langevin particle with drag coefficient and white-force covariance amplitude , detailed balance at temperature requires .
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Stochastic thermodynamics is a branch of statistical mechanics that extends classical thermodynamics to systems that are small enough to be influenced by random fluctuations, particularly at the microscopic or nanoscale. It combines principles of thermodynamics with stochastic processes to describe the behavior of systems where thermal fluctuations play a significant role.