We investigate the transport properties of active particles undergoing a three-state run-and-tumble dynamics in one dimension, induced by nonreciprocal transition rates between self-propelling velocity states $\{-v,0,+v\}$ that explicitly break microscopic reversibility. Departing from conventional reciprocal models, our formulation introduces a minimal yet rich framework for studying nonequilibrium transport driven by internal state asymmetries. Using kinetic Monte Carlo simulations and analytical methods, we characterize the particle's transport properties across the transition-rates space. The model exhibits a variety of nonequilibrium behaviors, including ballistic transport, giant diffusion, and Gaussian or non-Gaussian transients, depending on the degree of asymmetry in the transition rates. We identify a manifold in transition-rate space where long-time diffusive behavior emerges despite the absence of microscopic reversibility. Exact expressions are obtained for the drift, effective diffusion coefficient, and moments of the position distribution. Our results establish how internal-state irreversibility governs macroscopic transport, providing a tractable framework to study nonequilibrium active motion beyond reciprocal dynamics.

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• Nonequilibrium statistical mechanics
• Stochastic processes
• Transport phenomena
• Self-propelled particles
• Fokker–Planck equation
• Monte Carlo methods
• Stochastic differential equations