We investigate a novel collisionless shock jump condition that constrains the cosmic-ray (CR) energy density. The injection process and the subsequent acceleration of CRs in the SNR shocks are closely related to the formation process of the collisionless shocks. The shock formation is caused by wave-particle interactions. Since the wave-particle interactions result in the energy exchange between electromagnetic fields and charged particles, the randomization of particles around the shock may occur at the rate given by the scalar product of the electric field and current. The randomization can be quantified by the entropy production. We find that order-of-magnitude estimates of the entropy production with reasonable strength of the electromagnetic fields in the SNR constrain the amount of the CR nuclei and ion temperatures. The constrained amount of the CR nuclei can be sufficient to explain the Galactic CRs. The ion temperature becomes half of the case without CRs. Future observations by XRISM and Athena can distinguish whether the SNR shock accelerates the CRs or not from the ion temperature observations.