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We study the applicability of the finite temperature effective potential in the equation of motion of a homogeneous “misaligned” scalar condensate $\phi$and find important caveats that severely restrict its domain of validity: (i) the of local thermodynamic equilibrium is in general not warranted, (ii) we show a direct relation between the effective potential and the thermodynamic entropy density $\mathcal{S}=-\partial V_{\mathrm{eff}}(T,\phi )/\partial T$, which entails that for a dynamical $\phi \left(t\right)$the entropy becomes a nonmonotonic function of time, (iii) parametric instabilities in both cases with and without spontaneous symmetry breaking lead to profuse particle production with nonthermal distribution functions, (iv) in the case of spontaneous symmetry breaking spinodal instabilities yield a complex effective potential, internal energy and , an untenable situation in thermodynamics. All these caveats associated with using the effective potential in the of the condensate cannot be overcome by finite temperature equilibrium resummation schemes. We argue that the dynamics of the condensate leads to decoupling and freeze-out from local thermodynamic equilibrium, and propose a quantum system approach based on unitary time evolution. It yields the correct equations of motion without the caveats of the effective potential, and provides a fully renormalized and thermodynamically consistent framework to study the dynamics of the “misaligned” condensate, with real and conserved energy and entropy amenable to numerical study. The evolution of the condensate leads to profuse with nonthermal distribution functions. Possible emergent asymptotic nonthermal states and eventual rethermalization are conjectured. Published by the American Physical Society2025 

We critically examine the applicability of the effective potential within dynamical situations and find, in short, that the answer is negative. An important caveat of the use of an effective potential in dynamical equations of motion is an explicit violation of energy conservation. An effective potential is introduced in a consistent quasistatic approximation, and its narrow regime of validity is discussed. Two ubiquitous instances in which even the adiabatic effective potential is not valid in dynamics are studied in detail: parametric amplification in the case of oscillating mean fields, and spinodal instabilities associated with spontaneous symmetry breaking. In both cases profuse particle production is directly linked to the failure of the effective potential to describe the dynamics. We introduce a consistent, renormalized, energy conserving dynamical framework that is amenable to numerical implementation. Energy conservation leads to the emergence of asymptotic highly excited, entangled stationary states from the dynamical evolution. As a corollary, decoherence via dephasing of the density matrix in the adiabatic basis is argued to lead to an emergent entropy, formally equivalent to the entanglement entropy. The results suggest novel characterization of asymptotic equilibrium states in terms of order parameter vs energy density. Published by the American Physical Society2024