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We study nonperturbative interaction corrections to the thermodynamicquantities of multichannel disordered wires in the presence of the Coulombinteractions. Within the replica nonlinear $\sigma$-model (NL$\sigma$M)formalism, they arise from nonperturbative soliton saddle points of theNL$\sigma$M action. The problem is reduced to evaluating the partition functionof a replicated classical one dimensional Coulomb gas. The state of the latterdepends on two parameters: the number of transverse channels in the wire,N_{ch}, and the dimensionless conductance, G(L_T), of a wire segment of lengthequal to the thermal diffusion length, L_T. At relatively high temperatures,$G(L_T) \gtrsim \ln N_{ch} $, the gas is dimerized, i.e. consists of boundneutral pairs. At lower temperatures, $\ln N_{ch} \gtrsim G(L_T) \gtrsim 1$,the pairs overlap and form a Coulomb plasma. The crossover between the tworegimes occurs at a parametrically large conductance $G(L_T) \sim \ln N_{ch}$,and may be studied independently from the perturbative effects. Specializing tothe high temperature regime, we obtain the leading nonperturbative correctionto the wire heat capacity. Its ratio to the heat capacity for noninteractingelectrons, C_0, is $\delta C/C_0\sim N_{ch}G^2(L_T)e^{-2G(L_T)}$.

Nonperturbative interaction effects in the thermodynamics of disordered wires