Entropy production (EP) is a fundamental measure of the thermodynamic inefficiency of a physical process. If there are no constraints on the rate matrices and Hamiltonians available to a driving protocol, one can transform a system from any initial Hamiltonian and state distribution to any final Hamiltonian and state distribution with zero EP. We investigate the minimal EP that must be incurred to implement such a transformation, if there are constraints on the set of allowed Hamiltonians and rate matrices. Our first result is that zero EP can be achieved even when the Hamiltonian has only a single controllable degree of freedom, as long as there are no constraints on the rate matrix (beyond detailed balance). We then derive non-trivial bounds on the EP that arise in the presence of simultaneous constraints on the Hamiltonian and the rate matrix. These bounds are determined by an effective non-equilibrium free energy, which reflects the work value of a distribution and Hamiltonian under a set of constraints. These results have implications for the thermodynamics of information, in that allow one to decompose acquired information into “useful” bits and “useless” bits.
BIOGRAPHY: Dr. Artemy Kolchinsky is a postdoctoral fellow at the Santa Fe Institute (New Mexico, USA).
His work lies at the intersection of information theory, statistical physics, and machine learning. He is particularly interested in using tools from statistical physics to derive fundamental bounds on the ability of real-world agents — whether protocells, organisms, or computers — to acquire and exploit information in adaptive ways. Link: https://www.santafe.edu/people/profile/artemy-kolchinsky