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We present a new equation of state for QCD in which the temperature $T$and the three chemical potentials for baryon number ${\mu }_B$, electric charge ${\mu }_Q$, and strangeness ${\mu }_S$can be varied independently. This result is based on a generalization of the $T^{\prime }$expansion scheme, thanks to which the diagonal ${\mu }_B$extrapolation was pushed up to a baryo-chemical potential ${\mu }_B/T\sim 3.5$for the first time. This considerably extended the coverage of the Taylor expansion, limited to ${\mu }_B/T<2.5–3$. As a consequence, we are able to offer a substantially larger coverage of the four-dimensional QCD phase diagram as well, compared to previously available Taylor expansion results. Our findings are based on new continuum estimated lattice data on the full set of second- and fourth-order fluctuations. 

Although calculations of QCD thermodynamics from first-principle lattice simulations are limited to zero net-density due to the fermion sign problem, several methods have been developed to extend the equation of state (EoS) to finite values of theB,Q,Schemical potentials. Taylor expansion aroundµ_i=0 (i = B,Q,S) enables to cover with confidence the region up toµ_i/T< 2.5. Recently, a new method has been developed to compute a 2D EoS in the (T,µ_B) plane. It was constructed through aT-expansion scheme (TExS), based on a resummation of the Taylor expansion, and is trusted up to densities aroundµ_B/T= 3.5. We present here the new 4D-TExS EoS, a generalization of the TExS to all 3 chemical potentials, expected to offer a larger coverage than the 4D Taylor expansion EoS. After explaining the basics of theT-Expansion Scheme and how it is generalized to multiple dimensions, we will present results for thermodynamic observables as functions of temperature and both finite baryon and strangeness chemical potentials.