This paper presents a dynamical theory of low-temperature shear deformation in amorphous solids, based on molecular-dynamics simulations of a two-dimensional, two-component noncrystalline system. The simulations reveal behavior typical of metallic glasses and other viscoplastic materials, including reversible elastic deformation at small stresses, irreversible plastic deformation at larger stresses, a stress threshold above which unbounded plastic flow occurs, and a strong dependence of the system's state on its deformation history. The theory introduces new state variables to describe the population of shear transformation zones, which are small regions susceptible to inelastic rearrangements under shear stress. These zones are governed by local entropic fluctuations in their volumes, and the theory accounts for many observed deformation dynamics, though it is a mean-field model that does not capture spatial correlations. The simulations show that the material behaves linearly elastically at low strain, becomes nonlinear and plastically deforms as strain increases, and exhibits a critical stress below which it "jams" and above which it flows plastically. The material shows history-dependent behavior, with plastic deformation occurring only after a certain stress threshold. The simulations also reveal that the material undergoes small dilation during deformation and that the inelastic strain is partially recoverable after unloading. The theory incorporates equations of motion for the density and internal states of shear transformation zones, with transition rates depending on the applied stress and the system's history. Microscopic observations indicate that the material's deformation is governed by non-affine molecular displacements, which are identified as shear transformation zones. These zones are small regions of molecules that rearrange in response to shear stress, and their behavior is described by a two-state model. The transition probability between these states depends on the free volume available for rearrangement, which is influenced by the applied stress. The theory predicts that the material's response is sensitive to the applied stress and exhibits memory effects due to the history of deformation. The simulations and theory show that the material's deformation is governed by a complex interplay of elastic and inelastic processes, with the inelastic strain increasing logarithmically as the applied stress approaches the yield stress. The theory also predicts that the material's response is history-dependent, with plastic deformation occurring in one direction but not in the opposite direction, indicating a Bauschinger effect. The results suggest that the material's microstructure is partially "memorized" through its deformation history, leading to anisotropic behavior in response to further shear. The theory provides a framework for understanding the dynamics of viscoplastic deformation in amorphous solids, though it is a simplified model that does not account for all aspects of the material's behavior.This paper presents a dynamical theory of low-temperature shear deformation in amorphous solids, based on molecular-dynamics simulations of a two-dimensional, two-component noncrystalline system. The simulations reveal behavior typical of metallic glasses and other viscoplastic materials, including reversible elastic deformation at small stresses, irreversible plastic deformation at larger stresses, a stress threshold above which unbounded plastic flow occurs, and a strong dependence of the system's state on its deformation history. The theory introduces new state variables to describe the population of shear transformation zones, which are small regions susceptible to inelastic rearrangements under shear stress. These zones are governed by local entropic fluctuations in their volumes, and the theory accounts for many observed deformation dynamics, though it is a mean-field model that does not capture spatial correlations. The simulations show that the material behaves linearly elastically at low strain, becomes nonlinear and plastically deforms as strain increases, and exhibits a critical stress below which it "jams" and above which it flows plastically. The material shows history-dependent behavior, with plastic deformation occurring only after a certain stress threshold. The simulations also reveal that the material undergoes small dilation during deformation and that the inelastic strain is partially recoverable after unloading. The theory incorporates equations of motion for the density and internal states of shear transformation zones, with transition rates depending on the applied stress and the system's history. Microscopic observations indicate that the material's deformation is governed by non-affine molecular displacements, which are identified as shear transformation zones. These zones are small regions of molecules that rearrange in response to shear stress, and their behavior is described by a two-state model. The transition probability between these states depends on the free volume available for rearrangement, which is influenced by the applied stress. The theory predicts that the material's response is sensitive to the applied stress and exhibits memory effects due to the history of deformation. The simulations and theory show that the material's deformation is governed by a complex interplay of elastic and inelastic processes, with the inelastic strain increasing logarithmically as the applied stress approaches the yield stress. The theory also predicts that the material's response is history-dependent, with plastic deformation occurring in one direction but not in the opposite direction, indicating a Bauschinger effect. The results suggest that the material's microstructure is partially "memorized" through its deformation history, leading to anisotropic behavior in response to further shear. The theory provides a framework for understanding the dynamics of viscoplastic deformation in amorphous solids, though it is a simplified model that does not account for all aspects of the material's behavior.