  Thermodynamic tradeoff relations quantify the fundamental concept of "no free
lunch" in the physical world, suggesting that faster and more precise physical
processes come at a higher thermodynamic cost. The key elements in these
tradeoff relations are the thermodynamic uncertainty relation and speed limit,
which are closely related to information inequalities from which other tradeoff
relations are derived. Concentration inequalities are relations that complement
information inequalities in statistical analyses and have been widely used in
various fields. However, their role in thermodynamic tradeoff relations remains
unclear. This study develops thermodynamic concentration inequalities that
provide bounds for the distribution of observables in quantum and classical
Markov processes. We derive a set of tradeoff relations that generalise speed
limits and thermodynamic uncertainty relations from the developed thermodynamic
concentration inequalities. The derived tradeoff relations hold under minimal
assumptions of the underlying physical processes. This study clarifies the role
of concentration inequalities in thermodynamics, paving the way for deriving
new tradeoff relations.
