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The irreversibility in a statistical system is traced to its probabilistic evolution, and the molecular chaos assumption is not its unique consequence as is commonly believed. Under the assumption that the rate of change of the each microstate probability vanishes only as time diverges, we prove that the entropy of a system at constant energy cannot decrease with time.
We derive a generalization of the Second Law of Thermodynamics that uses Bayesian updates to explicitly incorporate the effects of a measurement of a system at some point in its evolution. By allowing an experimenters knowledge to be updated by the m
We generalize the second law of thermodynamics in its maximum work formulation for a nonequilibrium initial distribution. It is found that in an isothermal process, the Boltzmann relative entropy (H-function) is not just a Lyapunov function but also
A microscopic definition of the thermodynamic entropy in an isolated quantum system must satisfy (i) additivity, (ii) extensivity and (iii) the second law of thermodynamics. We show that the diagonal entropy, which is the Shannon entropy in the energ
We discuss the non-equilibrium properties of a thermally driven micromachine consisting of three spheres which are in equilibrium with independent heat baths characterized by different temperatures. Within the framework of a linear stochastic Langevi
It is shown that the laws of thermodynamics are extremely robust under generalizations of the form of entropy. Using the Bregman-type relative entropy, the Clausius inequality is proved to be always valid. This implies that thermodynamics is highly u