<i>Colloquium</i>: Statistical mechanics and thermodynamics at strong coupling: Quantum and classical
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Abstract
The statistical mechanical description of small systems staying in thermal\nequilibrium with an environment can be achieved by means of the Hamiltonian of\nmean force. In contrast to the reduced density matrix of an open quantum\nsystem, or the reduced phase-space probability density function of a classical\nopen system, the Hamiltonian of mean force not only characterizes the reduced\nstate but also contains full information about the thermodynamics of the\nconsidered open system. The resulting thermodynamic potentials all assume the\nform as the difference of the potentials for the total system and the bare\nenvironment in the absence of the system. In contrast to work as a mechanical\nnotion, one faces several problems with the definition of heat which turns out\nto be largely ambiguous in the case of strong coupling between system and\nenvironment. The general theory of the thermodynamics of open systems, in\nparticular, in view of strong coupling, is reviewed and illustrated with\nseveral examples. The vagueness of heat is discussed in the context of the\nambiguities in the definitions of a fluctuating internal energy and other\nfluctuating thermodynamic potentials.\n