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Shannon Meets Carnot: Generalized Second Thermodynamic Law
The classical thermodynamic laws fail to capture the behavior of systems with
energy Hamiltonian which is an explicit function of the temperature. Such
Hamiltonian arises, for example, in modeling information processing systems,
like communication channels, as thermal systems. Here we generalize the second
thermodynamic law to encompass systems with temperature-dependent energy
levels, , where denotes averaging over
the Boltzmann distribution and reveal a new definition to the basic notion of
temperature. This generalization enables to express, for instance, the mutual
information of the Gaussian channel as a consequence of the fundamental laws of
nature - the laws of thermodynamics