The authors propose a new definition of a natural invariant measure for trajectory segments of finite duration in a many-particle system, particularly focusing on the probability of fluctuations in shear stress in a nonequilibrium steady state. They derive an expression for the ratio of probabilities that the shear stress reverses sign over a finite time, violating the second law of thermodynamics. This formula is supported by computer simulations. The normalized natural invariant measure is defined using the expanding eigenvalues of the stability matrix and the Lyapunov exponents. The authors apply this measure to a nonequilibrium stationary state of a fluid under external shear, using the SLLOD equations to model the system. They find that the probability of observing a segment with a positive shear stress lasting a time τ is exponentially smaller than that of a segment with a negative shear stress, consistent with the second law of thermodynamics. The results are validated through molecular dynamics simulations, showing good agreement with the theoretical predictions. The authors suggest that this dynamical weight method could be useful for studying nonequilibrium statistical mechanics in realistic many-particle systems.The authors propose a new definition of a natural invariant measure for trajectory segments of finite duration in a many-particle system, particularly focusing on the probability of fluctuations in shear stress in a nonequilibrium steady state. They derive an expression for the ratio of probabilities that the shear stress reverses sign over a finite time, violating the second law of thermodynamics. This formula is supported by computer simulations. The normalized natural invariant measure is defined using the expanding eigenvalues of the stability matrix and the Lyapunov exponents. The authors apply this measure to a nonequilibrium stationary state of a fluid under external shear, using the SLLOD equations to model the system. They find that the probability of observing a segment with a positive shear stress lasting a time τ is exponentially smaller than that of a segment with a negative shear stress, consistent with the second law of thermodynamics. The results are validated through molecular dynamics simulations, showing good agreement with the theoretical predictions. The authors suggest that this dynamical weight method could be useful for studying nonequilibrium statistical mechanics in realistic many-particle systems.