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We propose a new model for hadrons with quantum mechanical attractive andrepulsive interactions sensitive to some spatial correlation length parameterinspired by Beth-Uhlenbeck quantum mechanical non-ideal gas model\cite{uhlenbeck1937quantum}. We confront the thermodynamics calculated usingour model with a corresponding recent lattice data at four different values ofthe baryon chemical potential, $\mu_{\mathtt{b}}= 0, 170, 340, 425~$MeV overtemperatures ranging from $130$ MeV to $200~$MeV and for five values for thecorrelation length ranging from $0$ to $0.2~$fm. For equilibrium temperaturesup to the vicinity of the chiral phase transition temperature $\simeq 160~$MeV,a decent fitting between the model and the lattice data is observed fordifferent values of $r$, especially at $(\mu_{\mathtt{b}}, r) = (170,0.05),(340,0.1)$, and $(340,0.15)$, where $\mu_{\mathtt{b}}$ is in MeV and $r$ is infm. For vanishing chemical potential, the uncorrelated model ($r=0$), whichcorresponds to ideal hadron resonance gas model seems to offer the best fit.The quantum hadron correlations seem to be more probable at non-vanishingchemical potentials, especially within the range $\mu_{\mathtt{b}}\in [170,340~$MeV$]$.

An approach of statistical corrections to interactions in hadron resonance gas