  $\mathrm{T}\overline{\mathrm{T}}$ deformation was originally proposed as an
irrelevant solvable deformation for 2d relativistic quantum field theories
(QFTs). The same family of deformations can also be defined for integrable
quantum spin chains which was first studied in the context of integrability in
AdS/CFT. In this paper, we construct such deformations for yet another type of
models, which describe a collection of particles moving in 1d and interacting
in an integrable manner. The prototype of such models is the Lieb-Liniger
model. This shows that such deformations can be defined for a very wide range
of systems. We study the finite volume spectrum and thermodynamics of the
$\mathrm{T}\overline{\mathrm{T}}$-deformed Lieb-Liniger model. We find that for
one sign of the deformation parameter $(\lambda<0)$, the deformed spectrum
becomes complex when the volume of the system is smaller than certain critical
value, signifying the break down of UV physics. For the other sign
$(\lambda>0)$, there exists an upper bound for the temperature, similar to the
Hagedorn behavior of the $\mathrm{T}\overline{\mathrm{T}}$ deformed QFTs. Both
behaviors can be attributed to the fact that $\mathrm{T}\overline{\mathrm{T}}$
deformation changes the size the particles. We show that for $\lambda>0$, the
deformation increases the spaces between particles which effectively increases
the volume of the system. For $\lambda<0$, $\mathrm{T}\overline{\mathrm{T}}$
deformation fattens point particles to finite size hard rods. This is similar
to the observation that the action of
$\mathrm{T}\overline{\mathrm{T}}$-deformed free boson is the Nambu-Goto action,
which describes bosonic strings -- also an extended object with finite size.

High Energy Physics - Theory;Statistical Mechanics;Exactly Solvable and Integrable Systems