20 problems

Symplectic camel conjecture for statistical physics. The principle of the symplectic camel might play a fundamental role in thermodynamics and statistical physics, including Bose–E…

Let $e(v,\theta,q,S)$ be the energy expressed in terms of the independent variables $(v,\theta,q,S)$, where $v$ is the specific volume, $\theta$ is the temperature, and $q,S$ are t…

Mild-knowledge conjecture. This situation often occurs within the mild knowledge regime, so that

Independence conjecture. The nonlinearity of the phenomenon is not related to the linearity of the nondissipative phenomenon. This claim concerns the distinction between nonlineari…

Jauch's conjecture. When this conservation hypothesis holds, heat can be locally written as

Let $(\mathbb{R}^N)^n$ be the phase space associated with a language-model geometrization, and let … be a differentiable extension of the language-model entropy function. The entro…

Let $\mathcal{W}$ be the vocabulary, let $\mathcal{S}_n=\mathcal{W}^n$ be the finite set of sentences of length $n$, and let a geometrization consist of an embedding…

Universality conjecture. These observed features occur universally in the spontaneously broken ${\cal PT}$-regimes of non-Hermitian systems: the signs of the heat supply or removal…

Let $n>0$ and $gamma>0$ denote the particle number density and inverse temperature, respectively, and let $k_B,e,m,c,h$ be the Boltzmann constant, elementary charge, particle mass,…

The model assumes a spherical surface Cauchy stress tensor (the membrane model) and constant surface tension. The generalized-surface-stress conjecture. Relaxing these assumptions…

A state is a normalized linear functional over an algebra of observables; in classical statistical mechanics this algebra is Abelian. The mean entropy is the quantity relevant to a…

Extension conjecture. Every theory with a “well-behaved” thermodynamics can be extended to a sharp theory with purification.

Let $\bar u=(\bar r,\bar p)$ be a limit solution of the hyperbolic system with boundary conditions, satisfying the Clausius inequality … for all $t\in[0,T]$, where $W(t)$ is the wo…

In the thermodynamic description, variables occur in conjugate pairs, such as pressure and volume; the source does not specify additional notation or a precise mathematical formula…

Microscopic thermodynamics conjecture. Thermodynamics with microscopic systems should start with a plain ordered commutative monoid $A$, and taking the macroscopic limit should cor…

Consider fundamental relations whose derivatives define a positive squared radial function, so that one can construct a characteristic circumference on which solutions of the assoc…

In the geometric-thermodynamic formulation considered here, solutions of the partial differential-equation system lie on a characteristic circumference in an abstract space constru…

Levitin–Toffoli equivalence conjecture. It should be possible to convert into mechanical work an amount of heat

Let a General Relativistic spacetime determine a gravitational field, and let its associated quantum states admit an effective thermodynamic description. Gravitational thermodynami…

Let Assumption 2 be the continuity assumption introduced in the paper's formulation of the third law of thermodynamics. The systems under consideration are classical spin systems a…