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Towards thermodynamics with $N_f=2+1+1$ twisted mass quarks

We present preliminary results achieved within a recently started project dealing with QCD thermodynamics in the presence of a fully dynamical second quark family. We are employing the Wilson twisted mass discretization. To reduce the amount of zero temperature simulations and the cost of analysis we have chosen the fixed-scale approach. We show a variety of basic thermodynamic observables for temperatures ranging from 158 to 633 MeV. Simulations were performed for three lattice spacings below 0.1 fm each and at a single value of the pion mass which allows a comparison with previously obtained $N_f=2$ results. We determine the chiral crossover temperature from the bare chiral susceptibility and show results for the gauge part of the trace anomaly.