Information processing is bounded by thermodynamic requisites. Efficiency aspects of isothermal small systems which process information in the midst of fluctuations are addressed from a geometric perspective. Molecular motors are isothermal small systems responsible for the maintenance of several spontaneous biomolecular processes in nature. These systems produce entropy continuously when poised in a non-equilibrium steady state and are known to break several limits of classical thermodynamics such as linear irreversibility. Entropy production, as described by an irreversible Fokker-Planck equation, measures the heat dissipated to a medium as information is erased. The amount of heat dissipated is the thermodynamic cost associated to logically irreversible operations and is divided into two contributions - heat cost to maintain the steady state and the excess heat cost of the control parameters variation. The optimal dissipation protocol is computed with respect to the control parameters variation and it's represented as a geodesic in the Poincaré plane of a Riemannian univariate statistical manifold. The Riemannian structure is naturally defined by integrating the fluctuations into the axioms of thermodynamics such that the physical observables are necessarily treated as stochastic quantities. Moreover, protocol efficiency is evaluated by the geometric invariants of the statistical manifold, namely, the Fisher information metric and the Amari-Chentsov tensor. The Fisher information metric in particular captures the total amount of fluctuations and dissipated heat. Finally, we present generalizations of information geometry based on Souriau's symplectic interpretation of thermodynamics and link them to the previous results on heat dissipation. A remarkable result stemming from this perspective is the equivalence between the Souriau-Fisher metric and a generalized heat capacity. This equivalence is interpreted in the context of information processing and complexity.

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Complex systems,Information Geometry,Fluctuations,Dissipation protocols,Thermodynamic uncertainty relations,Souriau-Fisher metric,Heat capacity