This paper proposes a new definition of a natural invariant measure for trajectory segments of finite duration in many-particle systems. Based on this, the authors derive an expression for the probability of fluctuations in shear stress in a fluid under nonequilibrium steady state. They obtain a formula for the ratio of probabilities that the shear stress reverses sign, violating the second law of thermodynamics. Computer simulations support this formula. The authors generalize a dynamical measure, which is not yet well founded but potentially useful for studying many-particle systems. They study a nonequilibrium stationary state of a fluid under external shear and conjecture a natural invariant measure for trajectory segments. This allows them to derive an expression for the ratio of probabilities to find the fluid on a phase space trajectory segment of duration τ in a dynamical state with induced shear stress in the direction or opposite to the externally imposed shear rate. The second case constitutes a violation of the second law of thermodynamics for finite τ. The normalized natural invariant measure is given by μ_i(τ) = exp[-∑_{n|+λ_{i,n}}τ] / ∑_i exp[-∑_{n|+λ_{i,n}}τ]. This measure is used to compute stationary state averages. The ratio of probabilities for a trajectory segment i to be in a state i or i^K (with reversed Lyapunov exponents) is given by an exponential function involving the sum of all Lyapunov exponents. The authors apply this ratio to determine the probability of occurrence of two dynamical states of segment i, with given pressure tensor values. They find that the probability of observing a state with positive pressure tensor is exponentially smaller than that of the corresponding state with negative pressure tensor. This is due to the generalized rate of entropy production during τ in the segment i. Molecular dynamics simulations were carried out for N=56 disks in d=2, using WCA potential and Lees-Edwards boundary conditions. The results show that the probability distribution of segment averages of the pressure tensor is approximately Gaussian, with a mean of about -1.116. The right-hand tail of the distribution corresponds to segments where the second law is violated. As τ increases, these violations decrease, and for τ→∞, the second law requires that P_xyτ < 0 and ⟨α⟩_τ > 0. The authors conclude that the proposed dynamical measure is a useful tool for studying nonequilibrium statistical mechanics, particularly for systems far from equilibrium. They also note that the results are consistent with the expected behavior of entropy production and the second law of thermodynamics.This paper proposes a new definition of a natural invariant measure for trajectory segments of finite duration in many-particle systems. Based on this, the authors derive an expression for the probability of fluctuations in shear stress in a fluid under nonequilibrium steady state. They obtain a formula for the ratio of probabilities that the shear stress reverses sign, violating the second law of thermodynamics. Computer simulations support this formula. The authors generalize a dynamical measure, which is not yet well founded but potentially useful for studying many-particle systems. They study a nonequilibrium stationary state of a fluid under external shear and conjecture a natural invariant measure for trajectory segments. This allows them to derive an expression for the ratio of probabilities to find the fluid on a phase space trajectory segment of duration τ in a dynamical state with induced shear stress in the direction or opposite to the externally imposed shear rate. The second case constitutes a violation of the second law of thermodynamics for finite τ. The normalized natural invariant measure is given by μ_i(τ) = exp[-∑_{n|+λ_{i,n}}τ] / ∑_i exp[-∑_{n|+λ_{i,n}}τ]. This measure is used to compute stationary state averages. The ratio of probabilities for a trajectory segment i to be in a state i or i^K (with reversed Lyapunov exponents) is given by an exponential function involving the sum of all Lyapunov exponents. The authors apply this ratio to determine the probability of occurrence of two dynamical states of segment i, with given pressure tensor values. They find that the probability of observing a state with positive pressure tensor is exponentially smaller than that of the corresponding state with negative pressure tensor. This is due to the generalized rate of entropy production during τ in the segment i. Molecular dynamics simulations were carried out for N=56 disks in d=2, using WCA potential and Lees-Edwards boundary conditions. The results show that the probability distribution of segment averages of the pressure tensor is approximately Gaussian, with a mean of about -1.116. The right-hand tail of the distribution corresponds to segments where the second law is violated. As τ increases, these violations decrease, and for τ→∞, the second law requires that P_xyτ < 0 and ⟨α⟩_τ > 0. The authors conclude that the proposed dynamical measure is a useful tool for studying nonequilibrium statistical mechanics, particularly for systems far from equilibrium. They also note that the results are consistent with the expected behavior of entropy production and the second law of thermodynamics.